Nonuniqueness of solutions of initial-value problems for parabolic p-Laplacian
Jiřı́ Benedikt, Vladimir Evgen'evich Bobkov, Petr Girg, Lukáš Kotrla, Peter Takáč · DOAJ (DOAJ: Directory of Open Access Journals) · 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.