A uniform bound for solutions to a thermo-diffusive system

TL;DR

This paper establishes uniform bounds over time for solutions to thermo-diffusive systems with classical and fractional diffusion, under specific growth conditions for nonlinearities, using a strategy inspired by Herrero, Lacey, and Velazquez.

Contribution

It provides new uniform bounds for solutions to thermo-diffusive systems with both classical and fractional diffusions, extending previous methods to broader nonlinear growth conditions.

Findings

Uniform bounds for classical diffusion systems with exponential nonlinearities.

Uniform bounds for fractional diffusion systems with sub-exponential nonlinearities.

Extension of Herrero, Lacey, and Velazquez's strategy to these systems.

Abstract

We obtain uniform in time bounds for the solutions to a class of thermo-diffusive systems with classical and fractional diffusions. In the classical diffusion case, the nonlinearities are assumed to be at most exponentially growing, while for the fractional diffusions they should grow slightly sub-exponentially. The proofs are based on the strategy of Herrero, Lacey, and Velazquez.