GLOBAL SMOOTH SOLUTIONS FOR TRIANGULAR REACTION-CROSS DIFFUSION SYSTEMS

Jessica Guerand (1) , Angeliki Menegaki (2) , Ariane Trescases (3)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 IHES - Institut des Hautes Études Scientifiques
3 IMT - Institut de Mathématiques de Toulouse UMR5219

For a class of reaction cross-diffusion systems of two equations with a cross-diffusion term in the first equation and with self-diffusion terms, we prove that the unique local smooth solution given by Amann theorem is actually global. This class of systems arises in Population dynamics, and extends the triangular Shigesada-Kawasaki-Teramoto system when general power-laws growth are considered in the reaction and diffusion rates.

Domaines: Equations aux dérivées partielles [math.AP]

Jessica Guerand, Angeliki Menegaki, Ariane Trescases. GLOBAL SMOOTH SOLUTIONS FOR TRIANGULAR REACTION-CROSS DIFFUSION SYSTEMS. 2022. ⟨hal-03581020⟩