Calculus of Variations and Geometric Measure Theory

G. Meglioli - D. D. Monticelli - F. Punzo

Nonexistence of solutions to quasilinear parabolic equations with a potential in bounded domains

created by meglioli on 13 Oct 2022


Published Paper

Inserted: 13 oct 2022
Last Updated: 13 oct 2022

Year: 2022


We are concerned with nonexistence results for a class of quasilinear parabolic differential problems with a potential in $\Omega\times(0,+\infty)$, where $\Omega$ is a bounded domain. In particular, we investigate how the behavior of the potential near the boundary of the domain and the power nonlinearity affect the nonexistence of solutions. Particular attention is devoted to the special case of the semilinear parabolic problem, for which we show that the critical rate of growth of the potential near the boundary ensuring nonexistence is sharp.