Geodesic
Noncontinuous solutions to degenerate parabolic inequalities
Electronic journal of differential equations, Tome 2015 (2015)
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.
Classification : 35D30, 35K51, 35R45
Keywords: parabolic equations, Cauchy problem, generalized solution 
@article{EJDE_2015__2015__a60,
     author = {Topolski,  Krzysztof A.},
     title = {Noncontinuous solutions to degenerate parabolic inequalities},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1322.35085},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a60/}
}
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AU  - Topolski,  Krzysztof A.
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JO  - Electronic journal of differential equations
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%A Topolski,  Krzysztof A.
%T Noncontinuous solutions to degenerate parabolic inequalities
%J Electronic journal of differential equations
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%F EJDE_2015__2015__a60
Topolski,  Krzysztof A. Noncontinuous solutions to degenerate parabolic inequalities. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a60/