In the paper, an inverse source problem for a time-fractional diffusion equation is formulated and proved. The topological sensitivity analysis method is presented. The considered problem is formulated as a topology optimization one. The proposed process leads to a non-iterative reconstruction algorithm can be applied for large class of cost functional. The unknown shape of the term source support

This paper studies the existence of weak solutions and their asymptotic behaviour to the initial boundary value problem for a multidimensional nonlinear Bresse system. The existence of the solutions of the problem is obtained by appliying Galerkin method. Then, we obtain an explicit decay rate estimation dependent on both the strain-caused stress and the damping terms by using the multiplier method

Single hidden layer feedforward neural networks can represent multivariate functions that are sums of ridge functions. These ridge functions are defined via an activation function and customizable weights. The paper deals with best non-linear approximation by such sums of ridge functions. Error bounds are presented in terms of moduli of smoothness. The main focus, however, is to prove that the bounds

In this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals

We presented a geometrical shock dynamics model to predict the behavior of weak converging shock waves in solid materials. Taking into consideration Mie–Grüneisen equation of state the analytical solution is obtained for the flow behind the converging shock-front propagating in solids. The analytical formaluas are also obtained for the shock velocity, pressure, density, particle velocity, temperature

This work discusses the existence of the limit as p goes to 1 of the nontrivial solutions to the one-dimensional problem: $$\begin{aligned} {\left\{ \begin{array}{ll} -\left( |u_x|^{p-2} u_x\right) _x = \lambda |{u}|^{{p}-2}{u} -|{u}|^{{q}-2}{u}&{} \quad 0< x < 1\\ u(0)=u(1)=0, &{} \end{array}\right. } \end{aligned}$$ where \(\lambda \) is a positive parameter and the exponents p, q satisfy \(1< p

Suppose \({\mathfrak R}\, \) is a 2,3-torsion free unital alternative ring having an idempotent element \(e_1\) \(\left( e_2 = 1-e_1\right) \) which satisfies \(x {\mathfrak R}\, \cdot e_i = \{0\} \Rightarrow x = 0\) \(\left( i = 1,2\right) \). In this paper, we aim to characterize the commuting maps. Let \(\varphi \) be a commuting map of \({\mathfrak R}\, \) so it is shown that \(\varphi (x) = zx

Let \(X = \{X_1,X_2, \ldots ,X_m\}\) be a system of smooth vector fields in \({{\mathbb R}^n}\) satisfying the Hörmander’s finite rank condition. We prove the following Sobolev inequality with reciprocal weights in Carnot-Carathéodory space \(\mathbb G\) associated to system X$$\begin{aligned} \left( \frac{1}{\int _{B_R} K(x)\; dx} \int _{B_R} |u|^{t} K(x) \; dx \right) ^{1/t} \le C\, R \left( \frac{1}{\int

In this paper, we investigate a mixed fractional integral boundary value problem with p(t)-Laplacian operator. Firstly, we derive the Green function through the direct computation and obtain the properties of Green function. For \(p(t)\ne \) constant, under the appropriate conditions of the nonlinear term, we establish the existence result of at least one positive solution of the above problem by means

In this paper, we prove the existence and uniqueness results of entropy solutions to a class of nonlinear parabolic p(u)-Laplacian problem with Fourier-type boundary conditions and \(L^1\)-data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.

The Cauchy problem for a class of hyperbolic operators with triple characteristics is analyzed. Some a priori estimates in Sobolev spaces with negative indexes are proved. Subsequently, an existence result for the Cauchy problem is obtained.

We establish asymptotic stability estimates for solutions to evolution problems with singular convection term. Such quantitative estimates provide a measure with respect to the time variable of the distance between the solution to a parabolic problem from the one of the its elliptic stationary counterpart.

We extend the algebraic construction of finite dimensional varying exponent \(L^{p(\cdot )}\) space norms, defined in terms of Cauchy polynomials to a more general setting, including varying exponent \(L^{p(\cdot )}\) spaces. This boils down to reformulating the Musielak–Orlicz or Nakano space norm in an algebraic fashion where the infimum appearing in the definition of the norm should become a (uniquely

The main aim of this paper to provide several scales of equivalent conditions for the bilinear Hardy inequalities in the case \(1< q, p_1, p_2<\infty \) with \(q \ge \max (p_1,p_2)\).

We study the existence of fast homoclinic orbits for the following damped vibration system \(\ddot{u}(t)+q(t)\dot{u}(t)+\nabla V(t,u(t))=0\); where \(q\in C(\mathbb {R},\mathbb {R})\) and \(V\in C^{1}(\mathbb {R}\times \mathbb {R}^{N},\mathbb {R})\) is of the type V(t,x)=-K(t,x)+W(t,x). A map K is not a quadratic form in x and W(t, x) is superquadratic in x.

In this paper we show how the method of parallel coordinates can be extended to three dimensions. As an application, we prove the conjecture of Antunes et al. (Adv Calc Var 10:357–380, 2017) that “the ball maximises the first Robin eigenvalue with negative boundary parameter among all convex domains of equal surface area” under the weaker restriction that the boundary of the domain is diffeomorphic

We use a variational approach to study existence and regularity of solutions for a Neumann p-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincaré inequality. Trace theorems for functions with bounded variation are applied in the definition of the variational functional and minimizers are shown to satisfy De Giorgi type conditions.

A Lagrangian version of the classical 1+1-dimensional Korteweg capillarity system is shown to encapsulate as a particular reduction an integrable Boussinesq equation. The associated integrability of the corresponding Eulerian capillarity system is set down. In turn, hidden integrability cases of the generalised Boussinesq equation are recorded associated with reduction of the Eulerian system to the

The Boltzmann equation for charge transport in monolayer graphene is numerically solved by using a discontinuous Galerkin method. The numerical fluxes are based on a uniform non oscillatory reconstruction. The numerical scheme has been tested by simulating the electron dynamics in a graphene field effect transistor. To the best of our knowledge the presented simulations are the first ones using a full

This notes studies the inhomogeneous non-linear Schrödinger equations with a harmonic potential $$\begin{aligned} i\partial _tu +\Delta u-|x|^2u+|x|^{b}|u|^{p-1}u=0. \end{aligned}$$ Indeed, following the methods of Fukuizumi and Ohta (Differ Integral Equ 16(6):691–706, 2003), Ohta (Funccialaj Ekvacioj 61:135–143, 2018), the non-linear and strong instability of standing waves are obtained in the two

The motivation of this study is to analyze the structure of the Riemann solutions for compressible hyperbolic system, so called logotropic system, with a Coulomb-type friction. The classical wave solutions of the Riemann problem (RP) for the logotropic system are structured explicitly for all cases. The system considered in this problem is hyperbolic in nature and the characteristic fields associated

In the present paper, we use a Lie group of transformations to obtain a class of similarity solutions to a problem of cylindrically symmetric strong shock waves propagating through one-dimensional, unsteady, and isothermal flow of a self-gravitating ideal gas under the influence of azimuthal magnetic field. The density of the ambient medium is assumed to be non-uniform ahead of the shock. The generators

Feng (Complexity, Art. 5139419, 2020) studied a thermoelastic laminated Timoshenko beam, where the heat conduction is given by Cattaneo’s law, as well as established the exponential and polynomial stabilities depending on the stability number \(\chi _\tau \). In this short paper, we consider the same system and show a lack of exponential stability when the stability number \(\chi _\tau \ne 0\), by

The paper is concerned with the IBVP of the Navier–Stokes equations. The goal is to evaluate the possible gap between the energy equality and the energy inequality deduced for a weak solution. This kind of analysis is new and the result is a natural continuation and improvement of a result obtained by the same authors in Crispo et al. (Some new properties of a suitable weak solution to the Navier–Stokes

The power graph \({\mathcal {P}}_{G}\) of a finite group G is the graph whose vertex set is G, two distinct vertices are adjacent if one is a power of the other. The order supergraph \({\mathcal {S}}_{G}\) of \({\mathcal {P}}_G\) is the graph with vertex set G, and two distinct vertices x, y are adjacent if o(x)|o(y) or o(y)|o(x). In this paper, we study the independence number of \({\mathcal {S}}_{G}\)

Control interventions and farming knowledge are equally important for plant disease control. In this article, a mathematical model has been derived using saturated response functions (nonlinear infection rate) for studying the dynamics of mosaic disease with farming awareness based roguing (removal of infected plants) and insecticide spraying . It is assumed that the use of roguing and spraying depend

Recently, systems of coupled renewal and retarded functional differential equations have begun to play a central role in complex and realistic models of population dynamics. In view of studying the local asymptotic stability of equilibria and (mainly) periodic solutions, we propose a pseudospectral collocation method to approximate the eigenvalues of the evolution operators of linear coupled equations

A mathematical model is proposed to assess the effects of a vaccine on the time evolution of a coronavirus outbreak. The model has the basic structure of SIRI compartments (susceptible–infectious–recovered–infectious) and is implemented by taking into account of the behavioral changes of individuals in response to the available information on the status of the disease in the community. We found that

A major challenge to successful crop production comes from viral diseases of plants that cause significant crop losses, threatening global food security and the livelihoods of countries that rely on those crops for their staple foods or source of income. One example of such diseases is a mosaic disease of plants, which is caused by begomoviruses and is spread to plants by whitefly. In order to mitigate

In this paper we aim to compare a popular numerical method with a new, recently proposed meshless approach for Heston PDE resolution. In finance, most famous models can be reformulated as PDEs, which are solved by finite difference and Monte Carlo methods. In particular, we focus on Heston model PDE and we solve it via radial basis functions (RBF) methods and alternating direction implicit. RBFs have

Plant–soil feedback is recognized as a causal mechanism for the emergence of vegetation patterns of the same species especially when water is not a limiting resource (e.g. humid environments) (Cartenì et al. in J Theor Biol 313:153–161, 2012. https://doi.org/10.1016/j.jtbi.2012.08.008; Marasco et al. in Bull Math Biol 76(11):2866–2883, 2014. https://doi.org/10.1007/s11538-014-0036-6). Nevertheless

In this paper, we develop a new disease-resistant mathematical model with a fraction of the susceptible class under imperfect vaccine and treatment of both the symptomatic and quarantine classes. With standard incidence when the associated reproduction threshold is less than unity, the model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable

In this paper we propose a non linear mathematical model describing the process of biodegradation of organic pollutants by means of fungi, and using glucose to sustain its metabolism and growth. Two aspects are investigated, firstly, we study equilibria and their stability for this model, and analyze the sensitivity of the persistence equilibrium with respect to some model parameters. Secondly, optimal

The objective is the study of the dynamics of a prey–predator model where the prey species can migrate between two patches. The specialist predator is confined to the first patch, where it consumes the prey following the simple law of mass action. The prey is further “endangered” in that it suffers from the strong Allee effect, assumed to occur due to the lowering of successful matings. In the second

The distributed delay was firstly proposed by Volterra in the 1930s since it is more realistic than discrete delay and has been introduced in many dynamical systems. In this paper, we establish a diffusive viral infection model with general incidence function and distributed delays subject to the homogeneous Neumann boundary conditions. Firstly, we prove the existence, uniqueness, positivity and boundedness

In this paper, it is shown how a combination of approximate symmetries of a nonlinear wave equation with small dissipations and singularity analysis provides exact analytic solutions. We perform the analysis using the Lie symmetry algebra of this equation and identify the conjugacy classes of the one-dimensional subalgebras of this Lie algebra. We show that the subalgebra classification of the integro-differential

In this paper, we consider a three species plankton–fish system that incorporates external toxicity and nonlinear harvesting. We consider that the growth of species are affected directly or indirectly by an external toxic substance and the feeding of the predator on the affected prey is considered as Holling type II functional response. All the possible biological feasible equilibrium points are determined

This paper provides a complete analysis of the stability of the steady-states for a three-dimensional system modeling cell dynamics after bone marrow transplantation in chronic myeloid leukemia. There are given results for both chronic and accelerated-acute phases of the disease.

We study the Dirichlet problem for a second order linear elliptic partial differential equation with discontinuous coefficients in unbounded domains. We establish an existence and uniqueness result.

This paper provides an account of results and methods from the theory of infinite groups admitting only finitely many normalizers of subgroups with a given property. Some new statements on this subject are also proved.

We consider a class of Dirichlet boundary problems for nonlinear degenerate elliptic equations with lower order terms. We prove, using symmetrization techniques, pointwise estimates for the rearrangement of the gradient of a solution u and integral estimates. As consequence, we get apriori estimates which show how the summability of the gradient of a solution increases when the summability of the datum

We prove that the range of sequence of vector measures converging widely satisfies a weak lower semicontinuity property, that the convergence of the range implies the strict convergence (convergence of the total variation) and that the strict convergence implies the range convergence for strictly convex norms. In dimension 2 and for Euclidean spaces of any dimensions, we prove that the total variation

The propagation of localised (in space-time) waves is analysed in the context of the dynamic theory of incompressible hyperelastic solids subject to body forces corresponding to a dual power-law substrate potential. A broad class of exact solutions is obtained which, under the assumption of slow modulation, incorporates Helmholtz-type solitary waves. The linear stability of these solutions is studied

We prove that some of the main results of linkage theory can be extended to a more general context in homological algebra. Our main result states that, under suitable circumstances, if one has a morphism among two objects in an abelian category, both equipped with a good resolution, then there is a canonical procedure to build up a good resolution for the cokernel of the dual morphism.

This article studies approximate controllability for a new class of semilinear control systems involving state-dependent delay in Hilbert space setting. We formulate some new sufficient conditions which ensure the existence of mild solution for the considered system via the Schauder fixed point theorem. We use the theory of fundamental solution and fractional powers of operator, to establish our major

We propose a general alternative regularization algorithm for solving the split equality fixed point problem for the class of quasi-pseudocontractive mappings in Hilbert spaces. We also illustrate the performance of our algorithm with numerical example and compare the result with some other algorithms in the literature in this direction. We found out that our algorithm requires a lesser number of iterations

Here is a corrected version of the Abstract.

We shall give the existence of a capacity solution to a nonlinear elliptic coupled system, whose unknowns are the temperature inside a semiconductor material, u, and the electric potential, \(\varphi \), the model problem we refer to is$$\begin{aligned} \left\{ \begin{array}{l} \Delta _p u+g(x,u)= \rho (u)|\nabla \varphi |^2 \quad \mathrm{in} \quad \Omega ,\\ {{\,\mathrm{div}\,}}(\rho (u)\nabla \varphi

Let R and S be two commutative rings with unity, let I be an ideal of S and \(\varphi : R \longrightarrow S\) be a ring homomorphism. In this paper, we give a characterization for the the amalgamated algebra \(R \bowtie ^\varphi I\) to be an Artinian ring.

In this study, a three species plant-pest-natural enemy compartmental model incorporating gestation delays for both pests and natural enemies in a polluted environment is proposed. The boundedness and positivity properties of the model are established. Equilibria and their stability analysis are carried out for all possible steady states. The existence of Hopf bifurcation in the system is analyzed

In this work, we consider the following nonlinear fractional differential equation$$\begin{aligned} {\left\{ \begin{array}{ll} -D^{\nu } u(t)=\lambda f(t,u(t))+e(t) \ \ \ in \ \ (0,1),\\ u^{(j)}(0)=0, \ \ 0\le j \le n-2, \ \ [D^{\alpha } u(t)]_{t=1}=0,\\ \end{array}\right. } \end{aligned}$$where \(\lambda >0\) is a parameter, \(n \ge 3\), \(n-1< \nu < n\), \(1 \le \alpha \le n-2\) and \(D^{\nu }\)

In this paper we investigate the uniqueness of potential recovery in the inverse Borg–Levinson problem, and our study deals with a model of its recovery. The article applies the theory of elliptic equations. Using the resolvent method, in fact, we obtain uniqueness conditions for potential recovery in the inverse Borg–Levinson problem with Newton’s boundary condition considered on a multidimensional

In this paper, we investigate the behavior of almost reverse lexicographic ideals with the Hilbert function of a complete intersection. More precisely, over a field K, we give a new constructive proof of the existence of the almost revlex ideal \(J\subset K[x_1,\ldots ,x_n]\), with the same Hilbert function as a complete intersection defined by n forms of degrees \(d_1\le \cdots \le d_n\). Properties

We prove the existence of an entropy solution for a class of nonlinear anisotropic elliptic unilateral problem associated to the following equation$$\begin{aligned} -\sum _{i=1}^{N} \partial _i a_i(x,u, \nabla u) -\sum _{i=1}^{N}\partial _{i}\phi _{i}( u)=\mu , \end{aligned}$$where the right hand side \(\mu \) belongs to \(L^{1}(\Omega )+ W^{-1, \vec {p'}}(\Omega )\). The operator \(-\sum _{i=1}^{N}

This paper extends the concept of a normal pair from commutative ring theory to the context of a pair of (associative unital) rings. This is done by using the notion of integrality introduced by Atterton. It is shown that if \(R \subseteq S\) are rings and \(D=(d_{ij})\) is an \(n\times n\) matrix with entries in S, then D is integral (in the sense of Atterton) over the full ring of \(n\times n\) matrices

Let \(f : A \rightarrow B\) be a ring homomorphism and J be an ideal of B. In this paper, we give a characterization of zero divisors of the amalgamation which is a generalization of Maimani’s and Yassemi’s work (see Maimani and Yassemi in J Pure Appl Algebra 212(1):168–174, 2008). Furthermore, we investigate the transfer of Prüfer domain concept to commutative rings with zero divisors in the amalgamation

Let \(\mathcal {A}\) be a standard operator algebra on a Banach space \(\mathcal {X}\) with \( \dim \mathcal {X}\ge 3\). In this paper, we determine the form of the bijective maps \(\phi :\mathcal {A}\longrightarrow \mathcal {A}\) satisfying$$\begin{aligned} \phi \left( \frac{1}{2}(AB^2+B^2A)\right) = \frac{1}{2}[\phi (A)\phi (B)^{2}+\phi (B)^{2}\phi (A)], \end{aligned}$$for every \(A,B \in \mathcal

In this paper, we consider a shift-dependent measure of generalized cumulative entropy and its dynamic (past) version in the case where the weight is a general non-negative function. Our results include linear transformations, stochastic ordering, bounds and aging classes properties and some relationships with other survival concepts. We also define the conditional weighted generalized cumulative entropy

We prove that in a Banach space with the metric approximation property the flat chains defined by De Pauw and Hardt (Am J Math 134:1–69, 2012) coincide with those of Adams (J Geom Anal 18:1–28, 2008).

In this paper, we use the gate condition on two multivalued k-demicontractive mappings to approximate a common solution of a finite family of monotone inclusion problem and fixed point problem in CAT(0) space. Furthermore, we propose a Halpern-type proximal point algorithm and prove its strong convergence to a common solution of a finite family of monotone inclusion problems and fixed point problem