Initial Blow-up of Solutions of Semilinear Parabolic Inequalities

TL;DR

This paper establishes an upper bound on the initial blow-up behavior of nonnegative solutions to certain semilinear parabolic inequalities, focusing on cases with moderate superlinear exponents.

Contribution

It provides new bounds on initial blow-up for solutions of semilinear parabolic inequalities with specific exponent ranges.

Findings

Derived an upper bound for initial blow-up behavior.

Applicable to inequalities with moderate superlinear exponents.

Enhances understanding of solution behavior near initial time.

Abstract

We obtain an upper bound on the initial blow-up of nonnegative solutions of second order semilinear parabolic inequalities when a superlinear exponent in the inequalities is not too large.