Krzysztof A. Topolski
Abstract:
We consider the initial value problem for degenerate parabolic
equations. We prove theorems on differential inequalities and
comparison theorems in unbounded domain. As a solution of differential
inequality we consider upper absolutely (lower absolutely) continuous
in t function (we admit discontinuity in time variable). In the last
section we compare our notion of subsolutions to the notion of viscosity
subsolutions smooth in space variable. By giving a counterexample we show that
upper absolutcontinuity plays crucial role in the equivalence of the two notions.
Submitted October 2, 2014. Published April 28, 2015.
Math Subject Classifications: 35D30, 35K51, 35R45.
Key Words: Parabolic equations; Cauchy problem; generalized solution.
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Krzysztof A. Topolski Institute of Mathematics University of Gdansk Wit Stwosz 57, 80-952 Gdansk, Poland email: matkt@mat.ug.edu.pl |
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