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Rothe's Method for Semilinear Parabolic Problems with Degeneration

✍ Scribed by Volker Pluschke

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
572 KB
Volume
156
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The paper deals with semilinear parabolic initial‐boundary value problems whereat the coefficient g(x, t) of the time derivative may vanish at a set of zero measure. Existence of a local weak solution of the problem is proved by means of semidiscretization in time. In order to omit a growth limitation for the nonlinearity we derive uniform boundedness of the approximates in L~∞~ (Q~T~). Moreover, the weak solution turns out to be continuous even in the points of degeneration.

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