Necessary Conditions for Local and Global Solvability of Non-Diagonal Degenerate Systems

Abstract

Cross-diffusion has been widely considered either in the mechanical description of diffusion or in the stochastic point process description of interacting populations, in the mathematical modelling of spatially structured epidemic or ecological systems and for the geographical diffusion of innovation. In this paper, specific attention is devoted to blowing-up solutions of some systems which may reflect either failures in the modelling or genuine phenomena like aggregation of populations. Furthemore, necessary conditions for local and global existence of solutions to the considered systems are presented.