相关论文: Boundary Value Problems for Linear PDEs with Varia…
Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general…
We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homogeneous Neumann boundary condition. All the leading coefficients are assumed to be only…
A large class of initial-boundary value problems of linear evolution partial differential equations formulated on the half-line is analyzed via the unified transform method. In particular, explicit formulae are presented for the generalized…
Model two-dimensional singular perturbed eigenvalue problem for Laplacian with frequently alternating type of boundary condition is considered. Complete two-parametrical asymptotics for the eigenelements are constructed.
In this note we devise and analyse well-posed variational formulations and operator theoretical methods for boundary value problems associated to the biharmonic operator. Of particular interest are Neumann type and over- and underdetermined…
In this paper, existence and localization results of $C^1$-solutions to elliptic Dirichlet boundary value problems are established. The approach is based on the nonlinear alternative of Leray-Schauder.
This paper studies an initial boundary value problem for a class of nonlinear Dirac equations with cubic terms and moving boundary. For the initial data with bounded $L^2$ norm and the suitable boundary conditions, the global existence and…
We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…
We consider Calder\'{o}n's inverse boundary value problems for a class of nonlinear Helmholtz Schr\"{o}dinger equations and Maxwell's equations in a bounded domain in $\R^n$. The main method is the higher-order linearization of the…
In this paper, we propose simple numerical algorithms for partial differential equations (PDEs) defined on closed, smooth surfaces (or curves). In particular, we consider PDEs that originate from variational principles defined on the…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
In this paper we consider the initial boundary value problem of the Korteweg-de Vries equation posed on a finite interval \begin{equation} u_t+u_x+u_{xxx}+uu_x=0,\qquad u(x,0)=\phi(x), \qquad 0<x<L, \ t>0 \qquad (1) \end{equation} subject…
We present an introduction to boundary value problems for Dirac-type operators on complete Riemannian manifolds with compact boundary. We introduce a very general class of boundary conditions which contains local elliptic boundary…
We derive explicit solution representations for linear, dissipative, second-order Initial-Boundary Value Problems (IBVPs) with coefficients that are spatially varying, with linear, constant-coefficient, two-point boundary conditions. We…
We study a model elliptic pseudo-differential equation and simplest boundary value problems for a half-space and a special cone in Sobolev--Slobodetskii spaces which have different smoothness with respect to separate variables. Sufficient…
This paper deals with some classes of Kirchhoff type problems on a double phase setting and with nonlinear boundary conditions. Under general assumptions, we provide multiplicity results for such problems in the case when the perturbations…
In this note we discuss an abstract framework for standard boundary value problems in divergence form with maximal monotone relations as "coefficients". A reformulation of the respective problems is constructed such that they turn out to be…
A bosonic Laplacian is a conformally invariant second order differential operator acting on smooth functions defined on domains in Euclidean space and taking values in higher order irreducible representations of the special orthogonal…
A definition of invariance in Lie's sense for a boundary value problem (BVP) with the basic evolution differential equations is proposed. A problem of group classification at a wide class of BVPs parameterized by arbitrary elements is…
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…