Geodesic
Nonuniqueness of solutions of initial-value problems for parabolic \(p\)-Laplacian
Electronic journal of differential equations, Tome 2015 (2015)
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.
Classification : 35B05, 35B30, 35K15, 35K55, 35K65
Keywords: quasilinear parabolic equations with p-Laplacian, nonuniqueness for initial-boundary value problem, sub- and supersolutions, comparison principle 
@article{EJDE_2015__2015__a32,
     author = {Benedikt,  Jiri and Bobkov,  Vladimir E. and Girg,  Petr and Kotrla,  Lukas and Takac,  Peter},
     title = {Nonuniqueness of solutions of initial-value problems for parabolic {\(p\)-Laplacian}},
     journal = {Electronic journal of differential equations},
     year = {2015},
     volume = {2015},
     zbl = {1515.35148},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a32/}
}
TY  - JOUR
AU  - Benedikt,  Jiri
AU  - Bobkov,  Vladimir E.
AU  - Girg,  Petr
AU  - Kotrla,  Lukas
AU  - Takac,  Peter
TI  - Nonuniqueness of solutions of initial-value problems for parabolic \(p\)-Laplacian
JO  - Electronic journal of differential equations
PY  - 2015
VL  - 2015
UR  - http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a32/
LA  - en
ID  - EJDE_2015__2015__a32
ER  - 
%0 Journal Article
%A Benedikt,  Jiri
%A Bobkov,  Vladimir E.
%A Girg,  Petr
%A Kotrla,  Lukas
%A Takac,  Peter
%T Nonuniqueness of solutions of initial-value problems for parabolic \(p\)-Laplacian
%J Electronic journal of differential equations
%D 2015
%V 2015
%U http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a32/
%G en
%F EJDE_2015__2015__a32
Benedikt,  Jiri; Bobkov,  Vladimir E.; Girg,  Petr; Kotrla,  Lukas; Takac,  Peter. Nonuniqueness of solutions of initial-value problems for parabolic \(p\)-Laplacian. Electronic journal of differential equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a32/