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 \({\mathcal {S}}_{G}\)

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 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

We prove the existence of solutions for a quasilinear elliptic system$$\begin{aligned} \left\{ \begin{array}{ll} -\text {div}\,\sigma (x,u,Du)&{}=f(x,u,Du)\quad \text {in}\;\varOmega ,\\ u&{}=0\quad \text {on}\;\partial \varOmega . \end{array} \right. \end{aligned}$$The results are obtained in Orlicz–Sobolev spaces by means of the Young measures.

Let G be a group. An automorphism \(\alpha \) of G is called a commuting automorphism if \(\alpha (x)x= x \alpha (x)\) for all \(x \in G\). The set of all commuting automorphisms of G is denoted by A(G). The set A(G) does not necessarily form a subgroup of the automorphism group of G. If A(G) form a subgroup, then we say G is an A-group. In this paper, we show that the direct product of two finite

In this talk we discuss some recent results I obtained for a class of nonlinear models in quantum mechanics. In particular we focus our attention to the nonlinear one-dimensional Schrodinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark–Wannier ladders of the linear equation become a dense energy spectrum because a cascade of bifurcations

A combination \(\varvec{a}+{\mathrm{i}}\varvec{b}\) where \({\mathrm{i}}^2=-1\) and \(\varvec{a},\,\varvec{b}\) are real vectors is called a bivector. Gibbs developed a theory of bivectors, in which he associated an ellipse with each bivector. He obtained results relating pairs of conjugate semi-diameters and in particular considered the implications of the scalar product of two bivectors being zero

We study non reflexive Orlicz spaces \(L^\varPsi \) and their Morse subspace \(M^\varPsi \), i.e. the closure of \(L^\infty \) in \(M^\varPsi \) to determine when \((M^\varPsi ,L^\varPsi )\) can be described as having an o–O type structure with respect to an equivalent norm on \(L^\varPsi \). Examples of classes of Young functions for which the answer is affirmative are provided, but also examples

The onset of instability in autonomous dynamical systems (ADS) of ordinary differential equations is investigated. Binary, ternary and quaternary ADS are taken into account. The stability frontier of the spectrum is analyzed. Conditions necessary and sufficient for the occurring of Hopf, Hopf–Steady, Double-Hopf and unsteady aperiodic bifurcations—in closed form—and conditions guaranteeing the absence

Let \(FL_{\nu }(K)\) be the finitary linear group of degree \(\nu \) over an associative ring K with unity. We prove that the torsion subgroups of \(FL_{\nu }(K)\) are locally finite for certain classes of rings K. A description of some f.g. solvable subgroups of \(FL_{\nu }(K)\) are given.

In this paper we study an optimal control problem for the mixed Dirichlet–Neumann boundary value problem for the strongly non-linear elliptic equation with p-Laplace operator and \(L^1\)-nonlinearity in their right-hand side. A density of surface traction u acting on a part of boundary of open domain is taken as a boundary control. The optimal control problem is to minimize the discrepancy between

An existence result is established for a class of quasilinear parabolic problem which is a diffusion type equations having continuous coefficients blowing up for a finite value of the unknown, a second hand \(\mu \in \mathcal {M}_{b}(Q)\) and an initial data \(u_{0}\in L^{1}(\Omega )\). We develop a technique which relies on the notion of a renormalized solution and an adequate regularization in time

In this paper we study the following fractional Hamiltonian systems$$\begin{aligned} \left\{ \begin{array}{lllll} -_{t}D^{\alpha }_{\infty }(_{-\infty }D^{\alpha }_{t}x(t))- L(t).x(t)+\nabla W(t,x(t))=0, \\ x\in H^{\alpha }(\mathbb {R}, \mathbb {R}^{N}), \end{array} \right. \end{aligned}$$where \(\alpha \in \left( {1\over {2}}, 1\right] ,\ t\in \mathbb {R}, x\in \mathbb {R}^N,\ _{-\infty }D^{\alpha

The aim of the present paper, how the people behave towards the offer of two products in two different patches. In this work, an innovation diffusion model with six-compartments for two different patches is proposed. There is a delay in the adoption of product-1 in patch-2 and delay of adoption of product-2 in patch-1. The entire population in both the patches is classified into three different groups

Motivated by the recent work of Asgari and Salimi Moghaddam (Rend Circ Mat Palermo II Ser 67:185–195, 2018) on the Riemannian geometry of tangent Lie groups, we prove that the tangent Lie group \({ TG}\) of a symplectic Lie group \((G,\omega )\) admits the structure of a symplectic Lie group. On \({ TG}\), we construct a left invariant symplectic form \({\widetilde{\omega }}\) which is induced from

It is shown that the lattice of all totally composition formations of finite groups is algebraic.

Data assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state (the forecast). The DA is an inverse and ill posed problem usually used to handle a huge amount of data, so, it is a big and computationally expensive problem. In the

This paper establishes the Hardy–Littlewood–Pólya inequalities, the Hardy inequalities and the Hilbert inequalities on amalgam spaces. Moreover, it also gives the mapping properties of the Mellin convolutions, the Hadamard fractional integrals and the Hausdorff operators on amalgam spaces. We establish these properties by some estimates for the operator norms of the dilation operators on amalgam spaces

First-passage time problems for continuous-time birth–death chains are considered. Recursive formulas for the moments of the first-exit time and of the first-passage time in terms of the potential coefficients are explicitly obtained. Making use of the probability current, some functional relations between transition probabilities for unrestricted and restricted continuous-time birth–death chains are

A multi-component, modulated NLS system is presented which admits symmetry reduction to a nonlinear subsystem that is shown to be integrable by application of its admitted Ermakov invariants and a novel class of reciprocal transformations.

In this paper we study the Dirichlet problem for two related equations involving the 1-Laplacian and a total variation term as reaction, namely: with homogeneous Dirichlet boundary conditions on \(\partial \varOmega \), where \(\varOmega \) is a regular, bounded domain in \(\mathbb {R}^N\). Here f is a measurable function belonging to some suitable Lebesgue space, while g(u) is a continuous function

The onset of double-diffusive convection in horizontal porous layers for the thermo-diffusive Soret phenomenon in the case of a generalized Darcy model including inertia term is investigated. Via a linearization principle recently introduced in Rionero (Atti Accad Naz Lincei Rend Cl Sci Fis Mat Natur 28:21–47, 2017) the coincidence between linear and nonlinear (global) stability thresholds of the thermo-solutal

Suppose that G is a finite group and H is a subgroup of G. H is said to be weakly s-semipermutable in G if there are a subnormal subgroup T of G and an s-semipermutable subgroup \(H_{ssG}\) of G contained in H such that \(G=HT\) and \(H\cap T\le H_{ssG}\); H is said to be an ss-quasinormal subgroup of G if there is a subgroup B of G such that \(G=HB\) and H permutes with every Sylow subgroup of B.

In previous papers we introduced a class of polynomials which follow the same recursive formula as the Lucas–Lehmer numbers, studying the distribution of their zeros and remarking that this distribution follows a sequence related to the binary Gray code. It allowed us to give an order for all the zeros of every polynomial \(L_n\). In this paper, the zeros, expressed in terms of nested radicals, are

We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue

In this paper, we consider the following nonlinear \(L_{\varphi }(\Omega )\)-elliplic problem:$$\begin{aligned} -\,\text{ div } a(x,u,\nabla u) =f -\text{ div } \phi (u)\quad \text{ in } \ \Omega , \end{aligned}$$in Musielak–Orlicz–Sobolev spaces, when only large monotonicity is satisfied, with \(f\in L^{1}(\Omega )\) and \(\phi (\cdot )\in C^{0}({\mathbb {R}},{\mathbb {R}}^{N}).\) By assuming that

Bäcklund transformations are applied to study the Gross–Pitaevskii equation. Supported by previous results, a class of Bäcklund transformations admitted by this equation are constructed. Schwarzian derivative as well as its invariance properties turn out to represent a key tool in the present investigation. Examples and explicit solutions of the Gross–Pitaevskii equation are obtained.