Nonuniqueness of solutions of initial-value problems for parabolic p-Laplacian

• Main Authors: Jiri Benedikt, Vladimir E. Bobkov, Petr Girg, Lukas Kotrla, Peter Takac
• Format: Article
• Language: English
• Published: Texas State University 2015-02-01
• Series: Electronic Journal of Differential Equations
• Subjects: Quasilinear parabolic equations with p-Laplacian; nonuniqueness for initial-boundary value problem; sub- and supersolutions; comparison principle
• Online Access: http://ejde.math.txstate.edu/Volumes/2015/38/abstr.html
• ISSN: 1072-6691

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.