Krzysztof A. Topolski
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
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