Discrete maximum principle in parabolic boundary-value problems

Discrete Maximum Principle and Adequate Discretizations of Linear Parabolic Problems

In this paper, we analyze the connections between the different qualitative properties of numerical solutions of linear parabolic problems with Dirichlet-type boundary condition. First we formulate the qualitative properties for the differential equations and shad light on their relations. Then we show how the well-known discretization schemes can be written in the form of a one-step iterative ...

A Generalized Maximum Principle for Boundary Value Problems for Degenerate Parabolic Operators with Discontinuous Coefficients

In [14] M.G.Platone Garroni has extended the classical generalized maximum principle (see, for instance, [15]), when the coefficients of the operator are discontinuous, to subsolutions of elliptic linear second order equations with mixed type boundary unilateral conditions, that is, on a portion of the boundary ∂Ω of Ω, the values of the solution are assigned, while on the other part a unilater...

Discrete Boundary-value Problems

We consider multivariate sequences, deened by a partial linear recurrence equation together with appropriate boundary conditions. The domain of deenition of these sequences is the rst orthant of the integer lattice, restricted in some dimensions to an initial segment of the nonnegative integers. By means of the kernel method we obtain an explicit expression for the generating function of the so...

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