Solution of a class of reaction-diffusion systems via logarithmic Sobolev inequality

TL;DR

This paper establishes the global existence, uniqueness, and positivity of weak solutions for certain reaction-diffusion systems using logarithmic Sobolev inequalities and exponential integrability conditions.

Contribution

It introduces a novel approach leveraging logarithmic Sobolev inequalities to analyze reaction-diffusion systems in chemical kinetics.

Findings

Proved global existence of solutions under specified conditions

Established uniqueness and positivity of solutions

Applied logarithmic Sobolev inequality to reaction-diffusion systems

Abstract

We study global existence, uniqueness and positivity of weak solutions of a class of reaction-diffusion systems of chemical kinetics type, under the assumptions of logarithmic Sobolev inequality and appropriate exponential integrability of the initial data.