NONUNIQUENESS OF SOLUTIONS OF INITIAL-VALUE PROBLEMS FOR PARABOLIC p-LAPLACIAN

作者：Benedikt Jiri^*; Bobkov Vladimir E; Girg Petr; Kotrla Lukas; Takac Peter

来源：Electronic Journal of Differential Equations, 2015, 38.

• Quasilinear parabolic equations with p-Laplacian
• nonuniqueness for initial-boundary value problem
• sub- and supersolutions
• comparison principle

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.

• 出版日期2015-2-10