The Initial Boundary Value Problem of a Parabolic System

Degenerate Parabolic Initial-Boundary Value Problems*

in Hilbert space and their realizations in function spaces as initial-boundary value problems for partial differential equations which may contain degenerate or singular coefficients. The Cauchy problem consists of solving (1.1) subject to the initial condition Jdu(0) = h. We are concerned with the case where the solution is given by an analytic semigroup; it is this sense in which the Canchy p...

Initial - Boundary Value Problems for Parabolic Equations

Parallel algorithm for spatially one-and two-dimensional initial-boundary-value problem for a parabolic equation

The importance of the boundary-value problems (BVP) for engineering applications attracts and motivates continuous development of fast numerical algorithms for its solution. A number of various approaches have been suggested, such as finite elements methods, fast Fourier transform methods, multigrids methods and difference methods (e.g. [1, 2, 3, 5, 6, 7, 8, 10]), etc. Some theoretical aspects ...

The Initial Dirichlet Boundary Value Problem for General Second Order Parabolic Systems in Nonsmooth Manifolds

In a series of recent papers [1], [2], [3], [4], [5] we have initiated the study of boundary value problems for (variable coefficients, second order, strongly) elliptic PDE’s in nonsmooth subdomains of Riemannian manifolds via integral equation methods. Here we take the first steps in the direction of extending this theory to initial boundary value problems (IBV P ’s) for variable coefficient (...

Semidiscrete-Least Squares Methods for a Parabolic Boundary Value Problem

In this paper some approximate methods for solving the initial-boundary value problem for the heat equation in a cylinder under homogeneous boundary conditions are analyzed. The methods consist in discretizing with respect to time and solving approximately the resulting elliptic problem for fixed time by least squares methods. The approximate solutions will belong to a finite-dimensional subspa...