Noncontinuous solutions to degenerate parabolic inequalities
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 disco...
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| Format: | Article |
| Language: | English |
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Texas State University
2015-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/113/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |