Related papers: Initial-boundary value problems for linear PDEs: t…

In this paper we consider an initial boundary value problem for a semilinear parabolic equation with absorption and nonlinear nonlocal Neumann boundary condition. We prove comparison principle, the existence theorem of a local solution and…

We consider the initial boundary value problem to equations of motion of an inextensible hanging string of finite length under the action of the gravity. We also consider the problem in the case without any external forces. In this problem,…

We investigate the qualitative properties of the weak solutions to the boundary value problems for the hyperbolic fourth-order linear equations with constant coefficients in the plane bounded domain convex with respect to characteristics.…

We focus on the initial boundary value problem for a general scalar balance law in one space dimension. Under rather general assumptions on the flux and source functions, we prove the well-posedness of this problem and the stability of its…

As a sequel to the paper [9], we study the existence and properties of Lipschitz solutions to the initial-boundary value problem of some forward-backward parabolic equations with diffusion fluxes violating Fourier's inequality.

Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this…

We establish existence and uniqueness results for initial-boundary value problems for transport equations in one space dimension with nearly incompressible velocity fields, under the sole assumption that the fields are bounded. In the case…

Motivated by many applications in complex domains with boundaries exposed to large topological changes or deformations, fictitious domain methods regard the actual domain of interest as being embedded in a fixed Cartesian background. This…

In this article, the authors survey and review the studies of boundary value problems for regular functions in Clifford analysis, which include theoretical foundations and useful methods. Its theoretical bases consist of the generalized…

The Cauchy- and periodic boundary value problem for the nonlinear Schroedinger equations in $n$ space dimensions [u_t - i\Delta u = (\nabla \bar{u})^{\beta}, |\beta|=m \ge 2, u(0)=u_0 \in H^{s+1}_x] is shown to be locally well posed for $s…

We consider operator-valued boundary value problems in $(0,2\pi)^n$ with periodic or, more generally, $\nu$-periodic boundary conditions. Using the concept of discrete vector-valued Fourier multipliers, we give equivalent conditions for the…

This paper is a continuation of our previous paper \cite{d1} on the initial boundary value problem for a nonconservative system appearing in elastodynamics in the space time domain $x>0,t>0$. There, the initial and boundary data were…

We establish well-posedness of initial-boundary value problems for continuity equations with BV (bounded total variation) coefficients. We do not prescribe any condition on the orientation of the coefficients at the boundary of the domain.…

In this paper, we study weakly nonlinear boundary value problems on infinite intervals. For such problems, we provide criteria for the existence of solutions as well as a qualitative description of the behavior of solutions depending on a…

We prove the existence of a fundamental solution of the Cauchy initial boundary value problem on the whole space for a parabolic partial differential equation with discontinuous unbounded first-order coefficient at the origin. We establish…

This work tackles an inverse boundary value problem for a $p$-Laplace type partial differential equation parametrized by a smoothening parameter $\tau \geq 0$. The aim is to numerically test reconstructing a conductivity type coefficient in…

We study the initial-boundary value problem of the stochastic Navier--Stokes equations in the half space. We prove the existence of weak solutions in the standard Besov space valued random processes when the initial data belong to the…

We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…

This paper is concerned with the initial boundary value problem for a nonconservative system of hyperbolic equation appearing in elastodynamics in the space time domain $x > 0, t > 0$. The number of boundary conditions to be prescribed at…

This paper studies the $d$-dimensional extension of a fictitious domain penalization technique that we previously proposed for Neumann or Robin boundary conditions. We apply Droniou's approach for non-coercive linear elliptic problems to…