Jiri Benedikt, Vladimir E. Bobkov, Petr Girg,
Lukas Kotrla, Peter Takac
Abstract:
We construct a positive solution to a quasilinear parabolic problem
in a bounded spatial domain with the p-Laplacian and a nonsmooth
reaction function. We obtain nonuniqueness for zero initial data.
Our method is based on sub- and supersolutions and
the weak comparison principle.
Using the method of sub- and supersolutions
we construct a positive solution to a quasilinear parabolic problem
with the p-Laplacian and a reaction function
that is non-Lipschitz on a part of the spatial domain.
Thereby we obtain nonuniqueness for zero initial data.
Submitted January 29, 2015. Published February 10, 2015.
Math Subject Classifications: 35B05, 35B30, 35K15, 35K55, 35K65.
Key Words: Quasilinear parabolic equations with p-Laplacian;
nonuniqueness for initial-boundary value problem;
sub- and supersolutions; comparison principle.
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Jiri Benedikt Department of Mathematics and NTIS Faculty of Applied Scences, University of West Bohemia Univerzitni 22, CZ-306 14 Plzen, Czech Republic email: benedikt@kma.zcu.cz | |
Vladimir E. Bobkov Fachbereich Mathematik Universitat Rostock, Germany email: vladimir.bobkov@uni-rostock.de | |
Petr Girg Department of Mathematics and NTIS Faculty of Applied Scences, University of West Bohemia Univerzitni 22, CZ-306 14 Plzen, Czech Republic email: pgirg@kma.zcu.cz | |
Lukas Kotrla Department of Mathematics and NTIS Faculty of Applied Scences, University of West Bohemia Univerzitni 22, CZ-306 14 Plzen, Czech Republic email: kotrla@ntis.zcu.cz | |
Peter Takac Fachbereich Mathematik Universitat Rostock Germany email: peter.takac@uni-rostock.de |
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