Related papers: Continuous dependence on the coefficients for a cl…
We study the curl-div-system with variable coefficients and a nonlocal homogenisation problem associated with it. Using, in part refining, techniques from nonlocal $H$-convergence for closed Hilbert complexes, we define the appropriate…
We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of…
We consider nonlinear Kolmogorov-Fokker-Planck type equations of the form \begin{equation}\label{abeqn} (\partial_t+X\cdot\nabla_Y)u=\nabla_X\cdot(A(\nabla_X u,X,Y,t)). \end{equation} The function…
We obtain conditions for the differentiability of weak solutions for a second-order uniformly elliptic equation in divergence form with a homogeneous co-normal boundary condition. The modulus of continuity for the coefficients is assumed to…
In this paper, we study the direct/indirect stability of locally coupled wave equations with local Kelvin-Voigt dampings/damping and by assuming that the supports of the dampings and the coupling coefficients are disjoint. First, we prove…
The authors consider non-autonomous dynamical behavior of wave-type evolutionary equations with nonlinear damping and critical nonlinearity. These type of waves equations are formulated as non-autonomous dynamical systems (namely,…
We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. We…
The paper deals with homogenization and higher order approximations of solutions to nonlocal evolution equations of convolution type whose coefficients are periodic in the spatial variables and random stationary in time. We assume that the…
A system of a first order history-dependent evolutionary variational-hemivariational inequality with unilateral constraints coupled with a nonlinear ordinary differential equation in a Banach space is studied. Based on a fixed point theorem…
An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged…
We produce uniform and decaying bounds in time for derivatives of the solution to the backwards Kolmogorov equation associated to a stochastic processes governed by a time dependent dynamics. These hold under assumptions over the…
In this paper we study the well-posedness of the Cauchy problem for a wave equation with multiplicities and space-dependent irregular coefficients. As in \cite{GR:14} in order to give a meaningful notion of solution, we employ the notion of…
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type…
This paper studies the Sobolev regularity estimates of weak solutions of a class of singular quasi-linear elliptic problems of the form $u_t - \mbox{div}[\mathbb{A}(x,t,u,\nabla u)]= \mbox{div}[{\mathbf F}]$ with homogeneous Dirichlet…
This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…
We study the coupling of a viscoelastic deformation governed by a Kelvin-Voigt model at equilibrium, based on the concept of second-grade nonsimple materials, with a plastic deformation due to volumetric swelling, described via a…
This paper is concerned with the decay estimate of solutions to the semilinear wave equation subject to two localized dampings in a bounded domain. The first one is of the nonlinear Kelvin-Voigt type and is distributed around a neighborhood…
We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent…
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…
In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…