Geodesic
Noncontinuous solutions to degenerate parabolic inequalities
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
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},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a60/}
}
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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/