Nonlinear parabolic problem with time fractional derivative

TL;DR

This paper studies a nonlinear time fractional parabolic equation involving the p-Laplacian and Hardy potential, establishing fundamental properties like comparison principles, existence, and blow-up behavior of solutions.

Contribution

It introduces new analysis for fractional parabolic problems with Hardy potentials, including existence, blow-up, and a priori estimates, expanding understanding of such complex equations.

Findings

Comparison principle established for the problem

Existence of global weak solutions proved

Finite-time blow-up characterized depending on Hardy constant

Abstract

Time fractional parabolic problem for p-Laplacian with double singular Hardy-type potential is considered. Comparison principle and appriory estimates for the weak solutions are proved. Existence of global weak solutions and finite-time blow-up are investigated depending on the optimal Hardy constant.