Global existence for reaction diffusion systems with strict balance Law and nonlinearities with non constant-sign and unlimited polynomial growth
arXiv:2302.02144
Abstract
The purpose of this paper is to prove global existence of solutions for general systems of reaction diffusion equations with nonlinearities for which only two main proprieties hold: Quasi-Positivity and balance law but with two difficulties: they change sign and with unlimited polynomial growth. We overcome the first difficulty by fixing the reaction sign after some time and the second one by using a judicious polynomial Lyapunov functional.