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Invariant measure for neutral stochastic functional differential equations with non-Lipschitz coefficients Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-02-18 Andriy Stanzhytsky, Oleksandr Misiats, Oleksandr Stanzhytskyi
In this work we study the long time behavior of nonlinear stochastic functional-differential equations of neutral type in Hilbert spaces with non-Lipschitz nonlinearities. We establish the existence of invariant measures in the shift spaces for such equations. Our approach is based on Krylov-Bogoliubov theorem on the tightness of the family of measures.
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Blow-up of solutions to semilinear wave equations with a time-dependent strong damping Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-02-18 Ahmad Z. Fino, Mohamed Ali Hamza
The paper investigates a class of a semilinear wave equation with time-dependent damping term (\begin{document}$ -\frac{1}{{(1+t)}^{\beta}}\Delta u_t $\end{document}) and a nonlinearity \begin{document}$ |u|^p $\end{document}. We will show the influence of the parameter \begin{document}$ \beta $\end{document} in the blow-up results under some hypothesis on the initial data and the exponent \begin{document}$
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A shape optimization problem constrained with the Stokes equations to address maximization of vortices Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-21 John Sebastian Simon, Hirofumi Notsu
We study an optimization problem that aims to determine the shape of an obstacle that is submerged in a fluid governed by the Stokes equations. The mentioned flow takes place in a channel, which motivated the imposition of a Poiseuille-like input function on one end and a do-nothing boundary condition on the other. The maximization of the vorticity is addressed by the \begin{document}$ L^2 $\end{document}-norm
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Local well-posedness of the coupled KdV-KdV systems on $ \mathbb{R} $ Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-21 Xin Yang, Bing-Yu Zhang
Inspired by the recent successful completion of the study of the well-posedness theory for the Cauchy problem of the Korteweg-de Vries (KdV) equation \begin{document}$ u_t +uu_x +u_{xxx} = 0, \quad \left. u \right |_{t = 0} = u_{0} $\end{document} in the space \begin{document}$ H^{s} (\mathbb{R}) $\end{document} (or \begin{document}$ H^{s} (\mathbb{T}) $\end{document}), we study the well-posedness
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The influence of the physical coefficients of a Bresse system with one singular local viscous damping in the longitudinal displacement on its stabilization Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-21 Mohammad Akil, Haidar Badawi
In this paper, we investigate the stabilization of a linear Bresse system with one singular local frictional damping acting in the longitudinal displacement, under fully Dirichlet boundary conditions. First, we prove the strong stability of our system. Next, using a frequency domain approach combined with the multiplier method, we establish the exponential stability of the solution if the three waves
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Exponential stabilization of the problem of transmission of wave equation with linear dynamical feedback control Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-21 Zhiling Guo, Shugen Chai
In this paper, we address exponential stabilization of transmission problem of the wave equation with linear dynamical feedback control. Using the classical energy method and multiplier technique, we prove that the energy of system exponentially decays.
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Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-10 Xilu Wang, Xiaoliang Cheng
In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some
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Stabilization of port-Hamiltonian systems with discontinuous energy densities Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-10 Jochen Schmid
We establish an exponential stabilization result for linear port-Hamiltonian systems of first order with quite general, not necessarily continuous, energy densities. In fact, we have only to require the energy density of the system to be of bounded variation. In particular, and in contrast to the previously known stabilization results, our result applies to vibrating strings or beams with jumps in
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Theoretical and computational decay results for a Bresse system with one infinite memory in the longitudinal displacement Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Mohamed Alahyane,Mohammad M. Al-Gharabli,Adel M. Al-Mahdi
In this paper, we consider a one-dimensional linear Bresse system with only one infinite memory term acting in the third equation (longitudinal displacements). Under a general condition on the memory kernel (relaxation function), we establish a decay estimate of the energy of the system. Our decay result extends and improves some decay rates obtained in the literature such as the one in [27], [4],
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Controllability results for Sobolev type $ \psi - $Hilfer fractional backward perturbed integro-differential equations in Hilbert space Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Ichrak Bouacida,Mourad Kerboua,Sami Segni
In this paper, the approximate controllability for Sobolev type \begin{document}$ \psi - $\end{document} Hilfer fractional backward perturbed integro-differential equations with \begin{document}$ \psi - $\end{document} fractional non local conditions in a Hilbert space are studied. A new set of sufficient conditions are established by using semigroup theory, \begin{document}$ \psi - $\end{document}Hilfer
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Stability properties for a problem of light scattering in a dispersive metallic domain Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Serge Nicaise,Claire Scheid
In this work, we study the well-posedness and some stability properties of a PDE system that models the propagation of light in a metallic domain with a hole. This model takes into account the dispersive properties of the metal. It consists of a linear coupling between Maxwell's equations and a wave type system. We prove that the problem is well posed for several types of boundary conditions. Furthermore
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Optimal control for stochastic differential equations and related Kolmogorov equations Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Ștefana-Lucia Aniţa
This paper concerns a stochastic optimal control problem with feedback Markov inputs. The problem is reduced to a deterministic optimal control problem for a Kolmogorov equation where the control for the deterministic problem is of open-loop type. The existence of an optimal control is proved for the deterministic control problem in a particular case. A maximum principle and some first order necessary
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Stability of a damped wave equation on an infinite star-shaped network Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Ahmed Bchatnia,Amina Boukhatem
In this paper, we study the stability of an infinite star-shaped network of a linear viscous damped wave equation. We prove that, under some conditions, the whole system is asymptotically stable. Moreover we give a decay rate of the energy of the solution. Our technique is based on a frequency domain method.
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A general decay result for the Cauchy problem of plate equations with memory Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Salim A. Messaoudi,Ilyes Lacheheb
In this paper, we investigate the general decay rate of the solutions for a class of plate equations with memory term in the whole space \begin{document}$ \mathbb{R}^n $\end{document}, \begin{document}$ n\geq 1 $\end{document}, given by \begin{document}$ \begin{equation*} u_{tt}+\Delta^2 u+ u+ \int_0^t g(t-s)A u(s)ds = 0, \end{equation*} $\end{document} with \begin{document}$ A = \Delta $\end{document}
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On the effect of perturbations in first-order optimization methods with inertia and Hessian driven damping Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Hedy Attouch,Jalal Fadili,Vyacheslav Kungurtsev
Second-order continuous-time dissipative dynamical systems with viscous and Hessian driven damping have inspired effective first-order algorithms for solving convex optimization problems. While preserving the fast convergence properties of the Nesterov-type acceleration, the Hessian driven damping makes it possible to significantly attenuate the oscillations. To study the stability of these algorithms
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On the Cauchy problem for a derivative nonlinear Schrödinger equation with nonvanishing boundary conditions Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Phan Van Tin
In this paper we consider the Schrödinger equation with nonlinear derivative term. Our goal is to initiate the study of this equation with non vanishing boundary conditions. We obtain the local well posedness for the Cauchy problem on Zhidkov spaces \begin{document}$ X^k( \mathbb{R}) $\end{document} and in \begin{document}$ \phi+H^k( \mathbb{R}) $\end{document}. Moreover, we prove the existence of
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Local null controllability for a parabolic equation with local and nonlocal nonlinearities in moving domains Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 André da Rocha Lopes,Juan Límaco
In this paper, we establish a local null controllability result for a nonlinear parabolic PDE with local and nonlocal nonlinearities in a domain whose boundary moves in time by a control force with a multiplicative part acting on a prescribed subdomain. We prove that, if the initial data is sufficiently small and the linearized system at zero satisfies an appropriate condition, the equation can be
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Exact controllability and stabilization for a general internal wave system of Benjamin-Ono type Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 José R. Quintero,Alex M. Montes
In this work we consider the exact controllability and stabilization on a periodic domain for the generalized Benjamin-Ono type system for internal waves. The exact controllability of the linearized model is proved by using the moment method and spectral analysis. In order to get the same result for the nonlinear model, we use a fixed point argument in Sobolev spaces.
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Initial boundary value problem for a strongly damped wave equation with a general nonlinearity Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Hui Yang,Yuzhu Han
In this paper, a strongly damped semilinear wave equation with a general nonlinearity is considered. With the help of a newly constructed auxiliary functional and the concavity argument, a general finite time blow-up criterion is established for this problem. Furthermore, the lifespan of the weak solution is estimated from both above and below. This partially extends some results obtained in recent
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Pseudo $ S $-asymptotically Bloch type periodic solutions to a damped evolution equation Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Siqi Chen,Yong-Kui Chang,Yanyan Wei
This paper is mainly concerned with the existence of pseudo S-asymptotically Bloch type periodic solutions to damped evolution equations in Banach spaces. Some existence results for classical Cauchy conditions and nonlocal Cauchy conditions are established through properties of pseudo S-asymptotically Bloch type periodic functions and regularized families. The obtained results show that for each pseudo
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Mathematical analysis of an abstract model and its applications to structured populations (I) Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Mohamed Boulanouar
The first part of this works deals with an integro–differential operator with boundary condition related to the interior solution. We prove that the model is governed by a strongly continuous semigroup and we precise its growth inequality. In the second part of this works, we model the proliferation-quiescence phases through a system of first order equations. We also prove that the proliferation-quiescence
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On the stabilization for the high-order Kadomtsev-Petviashvili and the Zakharov-Kuznetsov equations with localized damping Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Roger P. de Moura,Ailton C. Nascimento,Gleison N. Santos
In this paper we prove the exponential decay of the energy for the high-order Kadomtsev-Petviashvili II equation with localized damping. To do that, we use the classical dissipation-observability method and a unique continuation principle introduced by Bourgain in [3] here extended for the high-order Kadomtsev-Petviashvili. A similar result is also obtained for the two-dimensional Zakharov-Kuznetsov
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Functional inequalities involving nonlocal operators on complete Riemannian manifolds and their applications to the fractional porous medium equation Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Nikolaos Roidos,Yuanzhen Shao
The objective of this paper is twofold. First, we conduct a careful study of various functional inequalities involving the fractional Laplacian operators, including nonlocal Sobolev-Poincaré, Nash, Super Poincaré and logarithmic Sobolev type inequalities, on complete Riemannian manifolds satisfying some mild geometric assumptions. Second, based on the derived nonlocal functional inequalities, we analyze
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On a class of differential quasi-variational-hemivariational inequalities in infinite-dimensional Banach spaces Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Savin Treanţă
A class of differential quasi-variational-hemivariational inequalities (DQVHI, for short) is studied in this paper. First, based on the Browder's result, KKM theorem and monotonicity arguments, we prove the superpositionally measurability, convexity and strongly-weakly upper semicontinuity for the solution set of a general quasi-variational-hemivariational inequality. Further, by using optimal control
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Optimal control problems governed by two dimensional convective Brinkman-Forchheimer equations Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Manil T. Mohan
The convective Brinkman-Forchheimer (CBF) equations describe the motion of incompressible viscous fluids through a rigid, homogeneous, isotropic, porous medium and is given by \begin{document}$ \partial_t{\boldsymbol{u}}-\mu \Delta{\boldsymbol{u}}+({\boldsymbol{u}}\cdot\nabla){\boldsymbol{u}}+\alpha{\boldsymbol{u}}+\beta|{\boldsymbol{u}}|^{r-1}{\boldsymbol{u}}+\nabla p = {\boldsymbol{f}},\ \nabla\
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Asymptotic behavior of the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Chunyan Zhao,Chengkui Zhong,Zhijun Tang
In this paper, we prove the existence of the global attractor for the wave equation with nonlocal weak damping, nonlocal anti-damping and critical nonlinearity.
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Local null controllability for a parabolic equation with local and nonlocal nonlinearities in moving domains Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 André da Rocha Lopes,Juan Límaco
In this paper, we establish a local null controllability result for a nonlinear parabolic PDE with local and nonlocal nonlinearities in a domain whose boundary moves in time by a control force with a multiplicative part acting on a prescribed subdomain. We prove that, if the initial data is sufficiently small and the linearized system at zero satisfies an appropriate condition, the equation can be
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Exact controllability and stabilization for a general internal wave system of Benjamin-Ono type Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 José R. Quintero,Alex M. Montes
In this work we consider the exact controllability and stabilization on a periodic domain for the generalized Benjamin-Ono type system for internal waves. The exact controllability of the linearized model is proved by using the moment method and spectral analysis. In order to get the same result for the nonlinear model, we use a fixed point argument in Sobolev spaces.
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Initial boundary value problem for a strongly damped wave equation with a general nonlinearity Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Hui Yang,Yuzhu Han
In this paper, a strongly damped semilinear wave equation with a general nonlinearity is considered. With the help of a newly constructed auxiliary functional and the concavity argument, a general finite time blow-up criterion is established for this problem. Furthermore, the lifespan of the weak solution is estimated from both above and below. This partially extends some results obtained in recent
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On the Cauchy problem for a derivative nonlinear Schrödinger equation with nonvanishing boundary conditions Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Phan Van Tin
In this paper we consider the Schrödinger equation with nonlinear derivative term. Our goal is to initiate the study of this equation with non vanishing boundary conditions. We obtain the local well posedness for the Cauchy problem on Zhidkov spaces \begin{document}$ X^k( \mathbb{R}) $\end{document} and in \begin{document}$ \phi+H^k( \mathbb{R}) $\end{document}. Moreover, we prove the existence of
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Pseudo $ S $-asymptotically Bloch type periodic solutions to a damped evolution equation Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Siqi Chen,Yong-Kui Chang,Yanyan Wei
This paper is mainly concerned with the existence of pseudo S-asymptotically Bloch type periodic solutions to damped evolution equations in Banach spaces. Some existence results for classical Cauchy conditions and nonlocal Cauchy conditions are established through properties of pseudo S-asymptotically Bloch type periodic functions and regularized families. The obtained results show that for each pseudo
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Well-posedness and stability of non-autonomous semilinear input-output systems Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Jochen Schmid
We establish well-posedness results for non-autonomous semilinear input-output systems, the central assumption being the scattering-passivity of the considered semilinear system. Along the way, we also establish global stability estimates. We consider both systems with distributed control and observation and systems with boundary control and observation, and we treat them in a unified manner. Applications
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Pullback attractors for weak solution to modified Kelvin-Voigt model Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Mikhail Turbin,Anastasiia Ustiuzhaninova
The paper is devoted to the investigation of the qualitative dynamics of weak solutions for the modified Kelvin-Voigt model on the base of the theory of pullback attractors for trajectory spaces. At first, for the studied model, an auxiliary problem is considered, its solvability in the weak sense is proved, and some solution estimates are established. Then, on the base of these estimates, a family
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Controller and asymptotic autonomy of random attractors for stochastic p-Laplace lattice equations Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Li Song,Yangrong Li,Fengling Wang
A non-autonomous random dynamical system is called to be controllable if there is a pullback random attractor (PRA) such that each fibre of the PRA converges upper semi-continuously to a nonempty compact set (called a controller) as the time-parameter goes to minus infinity, while the PRA is called to be asymptotically autonomous if there is a random attractor for another (autonomous) random dynamical
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Exponential stability and stabilization of fractional stochastic degenerate evolution equations in a Hilbert space: Subordination principle Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Arzu Ahmadova,Nazim I. Mahmudov,Juan J. Nieto
In this paper, we obtain a closed-form representation of a mild solution to the fractional stochastic degenerate evolution equation in a Hilbert space using the subordination principle and semigroup theory. We study aforesaid abstract fractional stochastic Cauchy problem with nonlinear state-dependent terms and show that if the Sobolev type resolvent families describing the linear part of the model
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Controllability for Schrödinger type system with mixed dispersion on compact star graphs Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Roberto de A. Capistrano–Filho,Márcio Cavalcante,Fernando A. Gallego
In this work we are concerned with solutions to the linear Schrödinger type system with mixed dispersion, the so-called biharmonic Schrödinger equation. Precisely, we are able to prove an exact control property for these solutions with the control in the energy space posed on an oriented star graph structure \begin{document}$ \mathcal{G} $\end{document} for \begin{document}$ T>T_{min} $\end{document}
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Optimal control of mixed local-nonlocal parabolic PDE with singular boundary-exterior data Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Jean-Daniel Djida,Gisèle Mophou,Mahamadi Warma
We consider parabolic equations on bounded smooth open sets \begin{document}$ {\Omega}\subset \mathbb{R}^N $\end{document} (\begin{document}$ N\ge 1 $\end{document}) with mixed Dirichlet type boundary-exterior conditions associated with the elliptic operator \begin{document}$ \mathscr{L} : = - \Delta + (-\Delta)^{s} $\end{document} (\begin{document}$ 0
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On analytic semigroup generators involving Caputo fractional derivative Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Piotr Grabowski
Our investigations are motivated by the well - posedness problem of some dynamical models with anomalous diffusion described by the Caputo spatial fractional derivative of order \begin{document}$ \alpha \in (1, 2) $\end{document}. We propose a characterization of an exponentially stable analytic semigroup generator using the inverse operator. This characterization enables us to establish the form of
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Impulsive conformable fractional stochastic differential equations with Poisson jumps Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Hamdy M. Ahmed
In this article, periodic averaging method for impulsive conformable fractional stochastic differential equations with Poisson jumps are discussed. By using stochastic analysis, fractional calculus, Doob's martingale inequality and Cauchy-Schwarz inequality, we show that the solution of the conformable fractional impulsive stochastic differential equations with Poisson jumps converges to the corresponding
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Blow-up of solutions to a viscoelastic wave equation with nonlocal damping Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Donghao Li,Hongwei Zhang,Shuo Liu,Qingiyng Hu
The viscoelastic wave equation with nonlinear nonlocal weak damping is considered. The local existence of solutions is established. Under arbitrary positive initial energy, a finite-time blow-up result is proved by a new modified concavity method.
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Exponential stability for a multi-particle system with piecewise interaction function and stochastic disturbance Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Yipeng Chen,Yicheng Liu,Xiao Wang
In this paper, a generalized Motsch-Tadmor model with piecewise interaction function is investigated, which can be viewed as a generalization of the model proposed in [9]. Our analysis bases on the connectedness of the underlying graph of the system. Some sufficient conditions are presented to guarantee the system to achieve flocking. Besides, we add a stochastic disturbance to the system and consider
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Persistence of superoscillations under the Schrödinger equation Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Elodie Pozzi,Brett D. Wick
The goal of this paper is to provide new proofs of the persistence of superoscillations under the Schrödinger equation. Superoscillations were first put forward by Aharonov and have since received much study because of connections to physics, engineering, signal processing and information theory. An interesting mathematical question is to understand the time evolution of superoscillations under certain
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The lifespan of solutions for a viscoelastic wave equation with a strong damping and logarithmic nonlinearity Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Menglan Liao
This paper deals with the following viscoelastic wave equation with a strong damping and logarithmic nonlinearity: \begin{document}$ u_{tt}-\Delta u+\int_0^tg(t-s)\Delta u(s)ds-\Delta u_t = |u|^{p-2}u\ln|u|. $\end{document} A finite time blow-up result is proved for high initial energy. Meanwhile, the lifespan of the weak solution is discussed. The present results in this paper complement and improve
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Long-time behavior of a size-structured population model with diffusion and delayed birth process Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Dongxue Yan,Xianlong Fu
This work focuses on the long time behavior for a size-dependent population system with diffusion and Riker type birth function. Some dynamical properties of the considered system is investigated by using \begin{document}$ C_0 $\end{document}-semigroup theory and spectral analysis arguments. Some sufficient conditions are obtained respectively for asymptotical stability, asynchronous exponential growth
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Boundedness of solutions in a quasilinear chemo-repulsion system with nonlinear signal production Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Runlin Hu,Pan Zheng,Zhangqin Gao
This paper deals with a quasilinear parabolic-elliptic chemo-repulsion system with nonlinear signal production \begin{document}$ \begin{eqnarray*} \label{1a} \left\{ \begin{split}{} & u_t = \nabla\cdot(\phi(u)\nabla u)+\chi\nabla\cdot(u(u+1)^{\alpha-1}\nabla v)+f(u), & (x,t)\in \Omega\times (0,\infty), \\ & 0 = \Delta v-v+u^{\beta}, & (x,t)\in \Omega\times (0,\infty), \end{split} \right. \end{eqnarray*}
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Telegraph systems on networks and port-Hamiltonians. Ⅲ. Explicit representation and long-term behaviour Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Jacek Banasiak,Adam Błoch
In this paper we present an explicit formula for the semigroup governing the solution to hyperbolic systems on a metric graph, satisfying general linear Kirchhoff's type boundary conditions. Further, we use this representation to establish the long term behaviour of the solutions. The crucial role is played by the spectral decomposition of the boundary matrix.
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Attractors for a class of extensible beams with strong nonlinear damping Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Eduardo Henrique Gomes Tavares,Vando Narciso
We concern to stablish the existence and qualitative properties of the compact global attractor associate to solutions of a class of extensible beam equations with strong nonlinear damping arising from the wave model proposed by Prestel [18].
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From low to high-and lower-optimal regularity of the SMGTJ equation with Dirichlet and Neumann boundary control, and with point control, via explicit representation formulae Evol. Equat. Control Theory (IF 1.5) Pub Date : 2022-01-01 Roberto Triggiani,Xiang Wan
We consider the linear third order (in time) PDE known as the SMGTJ-equation, defined on a bounded domain, under the action of either Dirichlet or Neumann boundary control \begin{document}$ g $\end{document}. Optimal interior and boundary regularity results were given in [1], after [41], when \begin{document}$ g \in L^2(0, T;L^2(\Gamma)) \equiv L^2(\Sigma) $\end{document}, which, moreover, in the canonical
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Stability estimate for a partial data inverse problem for the convection-diffusion equation Evol. Equat. Control Theory (IF 1.5) Pub Date : 2021-12-10 Soumen Senapati, Manmohan Vashisth
In this article, we study the stability in the inverse problem of determining the time-dependent convection term and density coefficient appearing in the convection-diffusion equation, from partial boundary measurements. For dimension \begin{document}$ n\ge 2 $\end{document}, we show the convection term (modulo the gauge term) admits log-log stability, whereas log-log-log stability estimate is obtained
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Two simple criterion to obtain exact controllability and stabilization of a linear family of dispersive PDE's on a periodic domain Evol. Equat. Control Theory (IF 1.5) Pub Date : 2021-12-10 Francisco J. Vielma leal, Ademir Pastor
In this work, we use the classical moment method to find a practical and simple criterion to determine if a family of linearized Dispersive equations on a periodic domain is exactly controllable and exponentially stabilizable with any given decay rate in \begin{document}$ H_{p}^{s}(\mathbb{T}) $\end{document} with \begin{document}$ s\in \mathbb{R}. $\end{document} We apply these results to prove that
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Convergence of random attractors towards deterministic singleton attractor for 2D and 3D convective Brinkman-Forchheimer equations Evol. Equat. Control Theory (IF 1.5) Pub Date : 2021-12-10 Kush Kinra, Manil T. Mohan
This work deals with the asymptotic behavior of the two as well as three dimensional convective Brinkman-Forchheimer (CBF) equations in an \begin{document}$ n $\end{document}-dimensional torus (\begin{document}$ n = 2, 3 $\end{document}): \begin{document}$ \frac{\partial\boldsymbol{u}}{\partial t}-\mu \Delta\boldsymbol{u}+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\alpha\boldsymbol{u}+\beta|\boldsy
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Controlled singular evolution equations and Pontryagin type maximum principle with applications Evol. Equat. Control Theory (IF 1.5) Pub Date : 2021-12-10 Xiao-Li Ding, Iván Area, Juan J. Nieto
Due to the propagation of new coronavirus (COVID-19) on the community, global researchers are concerned with how to minimize the impact of COVID-19 on the world. Mathematical models are effective tools that help to prevent and control this disease. This paper mainly focuses on the optimal control problems of an epidemic system governed by a class of singular evolution equations. The mild solutions
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Impulsive hemivariational inequality for a class of history-dependent quasistatic frictional contact problems Evol. Equat. Control Theory (IF 1.5) Pub Date : 2021-11-12 Furi Guo, Jinrong Wang, Jiangfeng Han
This paper deals with a class of history-dependent frictional contact problem with the surface traction affected by the impulsive differential equation. The weak formulation of the contact problem is a history-dependent hemivariational inequality with the impulsive differential equation. By virtue of the surjectivity of multivalued pseudomonotone operator theorem and the Rothe method, existence and
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Approximate controllability of neutral delay integro-differential inclusion of order $ \alpha\in (1, 2) $ with non-instantaneous impulses Evol. Equat. Control Theory (IF 1.5) Pub Date : 2021-11-12 Avadhesh Kumar, Ankit Kumar, Ramesh Kumar Vats, Parveen Kumar
This paper aims to establish the approximate controllability results for fractional neutral integro-differential inclusions with non-instantaneous impulse and infinite delay. Sufficient conditions for approximate controllability have been established for the proposed control problem. The tools for study include the fixed point theorem for discontinuous multi-valued operators with the \begin{document}$
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A special form of solution to half-wave equations Evol. Equat. Control Theory (IF 1.5) Pub Date : 2021-10-14 Hyungjin Huh
We investigate a special form of solution to the one-dimensional half-wave equations with particular forms of nonlinearities. Using the special form of solution involving Hilbert transform, the half-wave equations reduce to nonlocal nonlinear transport equation which can be solved explicitly.
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Boundary controllability for a coupled system of degenerate/singular parabolic equations Evol. Equat. Control Theory (IF 1.5) Pub Date : 2021-10-14 Brahim Allal, Abdelkarim Hajjaj, Jawad Salhi, Amine Sbai
In this paper we study the boundary controllability for a system of two coupled degenerate/singular parabolic equations with a control acting on only one equation. We analyze both approximate and null boundary controllability properties. Besides, we provide an estimate on the null-control cost. The proofs are based on a detailed spectral analysis and the use of the moment method by Fattorini and Russell
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$ L^p $-exact controllability of partial differential equations with nonlocal terms Evol. Equat. Control Theory (IF 1.5) Pub Date : 2021-10-14 Luisa Malaguti, Stefania Perrotta, Valentina Taddei
The paper deals with the exact controllability of partial differential equations by linear controls. The discussion takes place in infinite dimensional state spaces since these equations are considered in their abstract formulation as semilinear equations. The linear parts are densely defined and generate strongly continuous semigroups. The nonlinear terms may also include a nonlocal part. The solutions
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Robustness of global attractors: Abstract framework and application to dissipative wave equations Evol. Equat. Control Theory (IF 1.5) Pub Date : 2021-10-14 Sergey Dashkovskiy, Oleksiy Kapustyan
We establish local input-to-state stability and the asymptotic gain property for a class of infinite-dimensional systems with respect to the global attractor of the respective undisturbed system. We apply our results to a large class of dissipative wave equations with nontrivial global attractors.
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Sufficient conditions for the continuity of inertial manifolds for singularly perturbed problems Evol. Equat. Control Theory (IF 1.5) Pub Date : 2021-09-29 Ahmed Bonfoh
We consider a nonlinear evolution equation in the form \begin{document}$ {{\rm{U}}_t} + {{\rm{A}}_\varepsilon }{\rm{U}} + {{\rm{N}}_\varepsilon }{{\rm{G}}_\varepsilon }({\rm{U}}) = 0,\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left( {{{\rm{E}}_\varepsilon }} \right)$\end{document} together with its singular limit problem as \begin{document}$ \varepsilon\to 0 $\end{document} \begin{document}$ \begin{align*}
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Exponential stabilization of a linear Korteweg-de Vries equation with input saturation Evol. Equat. Control Theory (IF 1.5) Pub Date : 2021-09-29 Ahmat Mahamat Taboye, Mohamed Laabissi
This article deals with the issue of the exponential stability of a linear Korteweg-de Vries equation with input saturation. It is proved that the system is well-posed and the origin is exponentially stable for the closed loop system, by using the classical argument used in this kind of problems.