Boundary Value Problems with Discontinuities in the Spatial Variable

Unilateral Boundary Value Problems with Jump Discontinuities

Using the critical point theory of Szulkin (1986), we study elliptic problems with unilateral boundary conditions and discontinuous nonlinearities. We do not use the method of upper and lower solutions. We prove two existence theorems: one when the right-hand side is nondecreasing and the other when it is nonincreasing. 1. Introduction. In this paper, using the critical-point theory of Szulkin ...

Numerical Solving of Singularly Perturbed Boundary Value Problems with Discontinuities

One-dimensional convection-diffusion problem with interior layers caused by the discontinuity of data is considered. Though standard Galerkin finite element method (FEM) generates oscillations in the numerical solutions, we prove its convergence in the ε-weighted norm of the first order on a class of layer-adapted meshes. We use streamline-diffusion finite element method (SDFEM) in order to sta...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Boundary Value Problems for Linear PDEs with Variable Coefficients

A new method is introduced for studying boundary value problems for a class of linear PDEs with variable coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs with constant coefficients. As illustrative examples the following boundary value problems are solved: (a) A Dirichlet and a Neumann problem on the half line for th...

Hyperbolic Boundary Value Problems for Symmetric Systems with Variable Multiplicities

We extend the Kreiss–Majda theory of stability of hyperbolic initial– boundary-value and shock problems to a class of systems, notably including the equations of magnetohydrodynamics (MHD), for which Majda’s block structure condition does not hold: namely, simultaneously symmetrizable systems with characteristics of variable multiplicity, satisfying at points of variable multiplicity either a “...