Related papers: Nonlocal complement value problem for a global in …
We study the existence of non-trivial, non-negative periodic solutions for systems of singular-degenerate parabolic equations with nonlocal terms and satisfying Dirichlet boundary conditions. The method employed in this paper is based on…
Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…
Well-posedness of certain semilinear parabolic problems with nonlocal initial conditions is shown in time-weighted spaces. The result is applied to recover the initial states in semilinear parabolic problems with nonlinearities of…
We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We…
A boundary value problem for a fractional power $0 < \varepsilon < 1$ of the second-order elliptic operator is considered. The boundary value problem is singularly perturbed when $\varepsilon \rightarrow 0$. It is solved numerically using a…
We consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. The dependence on the spatial coordinates comes from the presence of a potential and of a function representing a…
In this article we propose a scheme for solving the coupled time-fractional nonlocal diffusion problem. The scheme consist of fractional Crank-Nicolson method with Galerkin finite element method (FEM) and Newton's method. We derive \emph{a…
The aim of this paper is to prove the existence of almost global weak solutions for the unsteady nonlinear elastodynamics system in dimension $d=2$ or $3$, for a range of strain energy density functions satisfying some given assumptions.…
We show an existence of a weak solution of a degenerate and/or singular semilinear elliptic boundary value (nonhomogeneous) problem lying between a given weak subsolution and a given weak supersolution. It has been applied for an existence…
We examine inverse problems for the variable-coefficient nonlocal parabolic operator $(\partial_t - \Delta_g)^s$, where $0 < s < 1$. This article makes two primary contributions. First, we introduce a novel entanglement principle for these…
We establish new Harnack estimates that defy the waiting-time phenomenon for global solutions to nonlocal parabolic equations. Our technique allows us to consider general nonlocal operators with bounded measurable coefficients. Moreover, we…
We consider a boundary value problem for the parabolic Lam\'e type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consists of recovering a vector-function, satisfying the…
We consider a linear parabolic problem with random elliptic operator in the usual Gelfand triple setting. We do not assume uniform bounds on the coercivity and boundedness constants, but allow them to be random variables. The parabolic…
In this paper, we introduce a general constructive method to compute solutions of initial value problems of semilinear parabolic partial differential equations on hyper-rectangular domains via semigroup theory and computer-assisted proofs.…
We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time…
We introduce a notion of quasilinear parabolic equations over metric measure spaces. Under sharp structural conditions, we prove that local weak solutions are locally bounded and satisfy the parabolic Harnack inequality. Applications…
We study a semilinear wave inequality with double damping on a complete noncompact Riemannian manifold. The considered problem involves a potential function $V$ depending on the space variable in front of the power nonlinearity and an…
This paper is concerned with a class of nonhomogeneous quasilinear elliptic system driven by the locally symmetric potential and the small continuous perturbations in the whole-space $\mathbb{R}^N$. By a variant of Clark's theorem without…
The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from being models for describing reaction-diffusion processes in several frameworks. A…
We study the Cauchy problem for the semilinear heat equation with the singular potential, called the Hardy-Sobolev parabolic equation, in the energy space. The aim of this paper is to determine a necessary and sufficient condition on…