Asymptotic behavior in reaction-diffusion systems: an L1 approach
In this talk, we will discuss the large time asymptotic behavior for a wide class of reaction-diffusion systems. They include the celebrated Lotka-Volterra systems and also models for the evolution of concentrations in reversible (bio-)chemical reactions. They share the commun difficulty that existence of global classical solutions is still an open problem. Only weak and poorly regular solutions (even not bounded) can be considered. The space turns out to be adequate to analyze their asymptotic behavior together with entropy estimates and, curiously, space-time estimates.
These results have been obtained in collaboration with T. Suzuki, H. Umakoshi, Y. Yamada, R. Zou.