Blow-up rates for higher-order semilinear parabolic equations with nonlinear memory term

TL;DR

This paper investigates the blow-up behavior and rates of solutions for higher-order semilinear parabolic equations with nonlocal memory terms, providing new theoretical insights and well-posedness results.

Contribution

It introduces blow-up rate estimates and Liouville-type theorems for equations with infinite memory nonlinearities, advancing understanding of solution behavior without positivity assumptions.

Findings

Established blow-up rates for equations with nonlocal memory.

Proved Liouville-type theorems for infinite memory nonlinearities.

Analyzed well-posedness of mild solutions.

Abstract

In this paper, we establish blow-up rates for higher-order semilinear parabolic equations with nonlocal in time nonlinearity with no positive assumption on the solution. We also give Liouville-type theorem for higher-order semilinear parabolic equation with infinite memory nonlinear term which plays the main tools to prove our blow-up rate result. Finally, we study the well-posedness of mild solutions.