ROTHE METHOD FOR SEMILINEAR PARABOLIC PROBLEMS WITH DEGENERATION

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(infinity)(Q(T*)). Moreover, the weak solution turns out to be continuous even in the points of degeneration.