Dung Le. Cross Diffusion Systems: Dynamics, Coexistence and Persistence

Berlin: de Gruyter, 2022. — 236 p.The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new finddings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenbergi inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.Preliminaries
Existence results for cross-diffusion systems
Scalar techniques and diagonalization
Existence of solutions to general elliptic systems
Existence of solutions to elliptic systems of two equations
Persistence in the dynamics of evolution processes