Turing instability analysis of a singular cross-diffusion problem

The population model by Busenberg and Travis is a paradigmatic in ecology tumor modeling because its ability to capture interesting phenomena such as segregation of populations. Its singular mathematical structure enforces the consideration regularized problems deduce properties fundamental existence solutions. In this article we perform weakly nonlinear stability analysis general class study convergence instability modes limit regularization parameter. We demonstrate with some specific examples that pattern formation observed problems, unbounded wave numbers, not present problem amplitude decay oscillations. also check results direct finite element simulations problem. For more information see https://ejde.math.txstate.edu/Volumes/2021/55/abstr.html