A note on the existence of global solutions for reaction-diffusion equations with almost-monotonic nonlinearities

TL;DR

This paper proves that reaction-diffusion equations with almost-monotonic nonlinearities have well-posed solutions that exist globally in various L^q spaces, ensuring their mathematical robustness.

Contribution

It establishes the global existence and well-posedness of solutions for a class of reaction-diffusion equations with almost-monotonic nonlinearities.

Findings

Solutions are well-posed in L^q spaces for all 1 ≤ q < ∞

Solutions are globally defined over time

The analysis extends understanding of reaction-diffusion equations with specific nonlinearities

Abstract

We show that reaction-diffusion equations with almost-monotonic nonlinear terms are well-posed in $L^q(\Omega)$ for each $1\leq q < \infty$ and the solutions are globally defined.