Well-Posedness for the Reaction-Diffusion Equation with Temperature in a critical Besov Space

TL;DR

This paper establishes the global well-posedness of a non-isothermal reaction-diffusion system in a critical Besov space, combining thermodynamics and energetic variational methods to analyze solutions near equilibrium.

Contribution

It introduces a new model for non-isothermal reaction-diffusion equations derived from thermodynamics and proves well-posedness in a critical Besov space for small initial data.

Findings

Global-in-time existence of solutions near equilibrium

Well-posedness in a critical Besov space

Model derivation from thermodynamic principles

Abstract

We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from non-equilibrium thermodynamics with the energetic variational approach we obtain a general system modeling the evolution of a non-isothermal chemical reaction with general mass kinetics. From this we recover a linearized model for a system close to equilibrium and we analyze the global-in-time well-posedness of the system for small initial data for a critical Besov space.