Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 38, pp. 1-7.
Nonuniqueness of solutions of initial-value problems for parabolic
p-Laplacian
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.
Show me the PDF file (211 KB),
TEX file, and other files for this article.
 |
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
|
|---|
Return to the EJDE web page