Pointwise bounds for the second initial-boundary value problem of parabolic type

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 (...

Initial - Boundary Value Problems for Parabolic Equations

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 Problem for Hyperbolic Equations

where Ji = 0 for x0 < 0. The problem is to find necessary and sufficient conditions on B(x, B) such that the initial-boundary value problem (1), (2), (3) is well-posed. Note that all theorems that a;re formulated below will also apply to the case when (1) is a general hyperbolic equation or a hyperbolic system of equations of arbitrary order provided that all components of the characteristic co...

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 ...