On a nonlocal degenerate parabolic problem

TL;DR

This paper investigates a class of nonlinear nonlocal degenerate parabolic equations, establishing conditions for solutions' existence and uniqueness, and analyzing their long-term behavior including extinction and decay properties.

Contribution

It provides new existence and uniqueness criteria for weak solutions and explores their asymptotic behavior, including finite time extinction and polynomial decay.

Findings

Existence and uniqueness conditions for weak solutions are established.

Solutions exhibit finite time extinction under certain conditions.

Solutions show polynomial decay as time approaches infinity.

Abstract

Conditions for the existence and uniqueness of weak solutions for a class of nonlinear nonlocal degenerate parabolic equations are established. The asymptotic behaviour of the solutions as time tends to infinity are also studied. In particular, the finite time extinction and polynomial decay properties are proved.