Related papers: Continuous dependence on the coefficients for a cl…
We analytically derive novel explicit integral representations for the solution of nonhomogeneous initial-boundary-value problems for a large category of evolution partial differential equations of Sobolev-Galpern type with generic…
The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous…
In the present paper, we are concerned with the semilinear viscoelastic wave equation subject to a locally distributed dissipative effect of Kelvin-Voigt type, posed on a bounded domain with smooth boundary. We begin with an auxiliary…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
We consider a quasi-variational inequality governed by a moving set. We employ the assumption that the movement of the set has a small Lipschitz constant. Under this requirement, we show that the quasi-variational inequality has a unique…
We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…
Time dependent quantum systems have become indispensable in science and its applications, particularly at the atomic and molecular levels. Here, we discuss the approximation of closed time dependent quantum systems on bounded domains, via…
In this note, we analyze an abstract evolution equation with time-dependent time delay and time-dependent delay feedback coefficient. We assume that the operator corresponding to the nondelayed part of the model generates an exponentially…
This paper is concerned with the initial-boundary value problem for an evolutionary variational inequality complying with three intrinsic properties: complete irreversibility, unilateral equilibrium of an energy and an energy conservation…
We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpose of this article is twofold: first, it aims at a…
In this article, we investigate the existence and properties of time-periodic solutions for damped evolutionary partial differential equations subject to periodic forcing. Particular emphasis is placed on configurations where the energy…
In this article we shall study the following elliptic system with coefficients: \begin{equation}\notag \left\{\begin{aligned} -\epsilon^2\Delta u +c(x)u=b(x)|v|^{q-1}v, &\text{ and } -\epsilon^2\Delta v +c(x)v=a(x) |u|^{p-1}u &&\text{in }…
We investigate the stabilization of a multidimensional system of coupled wave equations with only one Kelvin Voigt damping. Using a unique continuation result based on a Carleman estimate and a general criteria of Arendt Batty, we prove the…
We discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in…
We study the Cauchy problem associated to a family of nonautonomous semilinear equations in the space of bounded and continuous functions over R^d and in L^p-spaces with respect to tight evolution systems of measures. Here, the linear part…
Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framework…
The aim of this article is to study a Cahn-Hilliard model for a multicomponent mixture with cross-diffusion effects, degenerate mobility and where only one of the species does separate from the others. We define a notion of weak solution…
In this paper we study the stability problem of a tree of elastic strings with local Kelvin-Voigt damping on some of the edges. Under the compatibility condition of displacement and strain and continuity condition of damping coefficients at…
In this paper we prove a variation of constants formula for a non autonomous and non homogeneous Cauchy problems whenever the linear part is not densely defined and is not a Hille-Yosida operator. By using this variation of constants…
This short survey article stems from recent progress on critical cases of stochastic evolution equations in variational formulation with additive, multiplicative or gradient noises. Typical examples appear as the limit cases of the…