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...
| Main Author: | |
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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 |
| _version_ | 1818512629964996608 |
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| author | Krzysztof A. Topolski |
| author_facet | Krzysztof A. Topolski |
| author_sort | Krzysztof A. Topolski |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T23:49:36Z |
| format | Article |
| id | doaj.art-ee218920f96a479ab640ae428bd5b6f3 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T23:49:36Z |
| publishDate | 2015-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-ee218920f96a479ab640ae428bd5b6f32022-12-22T01:28:50ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-04-012015113,112Noncontinuous solutions to degenerate parabolic inequalitiesKrzysztof A. Topolski0 Univ. of Gdansk, Poland 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.http://ejde.math.txstate.edu/Volumes/2015/113/abstr.htmlParabolic equationsCauchy problemgeneralized solution |
| spellingShingle | Krzysztof A. Topolski Noncontinuous solutions to degenerate parabolic inequalities Electronic Journal of Differential Equations Parabolic equations Cauchy problem generalized solution |
| title | Noncontinuous solutions to degenerate parabolic inequalities |
| title_full | Noncontinuous solutions to degenerate parabolic inequalities |
| title_fullStr | Noncontinuous solutions to degenerate parabolic inequalities |
| title_full_unstemmed | Noncontinuous solutions to degenerate parabolic inequalities |
| title_short | Noncontinuous solutions to degenerate parabolic inequalities |
| title_sort | noncontinuous solutions to degenerate parabolic inequalities |
| topic | Parabolic equations Cauchy problem generalized solution |
| url | http://ejde.math.txstate.edu/Volumes/2015/113/abstr.html |
| work_keys_str_mv | AT krzysztofatopolski noncontinuoussolutionstodegenerateparabolicinequalities |