The local solution of a parabolic-elliptic equation with a nonlinear neumann boundary condition (1997).

Content Provider	CiteSeerX
Author	Pluschke, Volker Weber, Frank
Abstract	The evolution problem which is investigated shows the following special features : (i) The time derivative is multiplied by a coefficient which may vanish in certain time-dependent subdomains. Hence, the differential equation we consider is parabolic-elliptic. (ii) The Lr-function g(\Delta; \Delta; ¸), arising in the boundary condition Bu = g(\Delta; \Delta; u), is only assumed to be defined and bounded on f ¸ 2 R : j¸j R g. The local weak solvability is proven by means of the Rothe method which is based on a semidiscretization with respect to the time variable, whereby the given problem is approximated by a sequence of linear elliptic problems. In view of (ii), the approximations, obtained by solving these "discretized" problems, have to be estimated in L1 . For that purpose, we use a Moser-technique, where Lp-estimates uniformly approach the desired boundedness statement as p \Gamma! 1. For the treatment of the degenerate differential equation, this L1 -technique is combined with ...
File Format	PDF
Publisher Date	1997-01-01
Access Restriction	Open
Subject Keyword	Nonlinear Neumann Boundary Condition Local Solution Parabolic-elliptic Equation Differential Equation L1 Technique Linear Elliptic Problem Following Special Feature Rothe Method Local Weak Solvability Certain Time-dependent Subdomains Evolution Problem Desired Boundedness Statement Degenerate Differential Equation Lp-estimates Uniformly Approach Boundary Condition Bu
Content Type	Text