Existence of solutions to nonlinear parabolic equations via majorant integral kernel

TL;DR

This paper proves the existence of solutions for various complex nonlinear parabolic equations using a novel majorant kernel approach, extending previous methods to fractional, higher-order, and viscous Hamilton-Jacobi equations.

Contribution

It introduces a new application of the majorant kernel technique to establish solutions for a broad class of nonlinear parabolic equations, including fractional and higher-order types.

Findings

Existence of solutions for fractional semilinear parabolic equations.

Existence results for higher-order semilinear parabolic equations.

Application to viscous Hamilton-Jacobi equations.

Abstract

We establish the existence of solutions to the Cauchy problem for a large class of nonlinear parabolic equations including fractional semilinear parabolic equations, higher-order semilinear parabolic equations, and viscous Hamilton-Jacobi equations by using the majorant kernel introduced in [K. Ishige, T. Kawakami, and S. Okabe, Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 37 (2020), 1185--1209].