Gauss' hypergeometric series and heat production in a cylinder
Gaussian lower bounds for random walks from elliptic regularity
General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations
New general unique solvability conditions of the Cauchy problem for systems of general linear functional differential equations are established. The class of equations considered covers, in particular, linear equations with transformed argument, integro-differential equations, neutral type equations and their systems of an arbitrary order.
Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE)
In this paper we describe PDELab, an extensible C++ template library for finite element methods based on the Distributed and Unified Numerics Environment (Dune). PDELab considerably simplifies the implementation of discretization schemes for systems of partial differential equations by setting up global functions and operators from a simple element-local description. A general concept for incorporation of constraints eases the implementation of essential boundary conditions, hanging nodes and varying...
Gevrey problem for parabolic equations with changing time direction.
Global and non-global existence of solutions to a nonlocal and degenerate quasilinear parabolic system
The paper deals with positive solutions of a nonlocal and degenerate quasilinear parabolic system not in divergence form with null Dirichlet boundary conditions. By using the standard approximation method, we first give a series of fine a priori estimates for the solution of the corresponding approximate problem. Then using the diagonal method, we get the local existence and the bounds of the solution to this problem. Moreover, a necessary and sufficient condition for the non-global existence...
Green function for the heat equation with oblique boundary conditions in an angle