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Rothe's Method for Semilinear Parabolic Problems with Degeneration
Author(s) -
Pluschke Volker
Publication year - 1992
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19921560118
Subject(s) - mathematics , mathematical analysis , zero (linguistics) , order (exchange) , derivative (finance) , measure (data warehouse) , nonlinear system , set (abstract data type) , initial value problem , weak solution , boundary value problem , boundary (topology) , computer science , financial economics , philosophy , linguistics , physics , finance , quantum mechanics , database , economics , programming language
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.