Stationary patterns of strongly coupled prey--predator models
The author considers the strongly coupled system \[ -\text{div} (K(u)\nabla u)= G(u) \quad\text{in }\Omega, \qquad \frac {\partial u}{\partial n}= 0 \quad\text{on }\partial\Omega. \tag{1} \] The author establishes a priori upper and lower bounds for positive solutions of (1), and studies the non-existence of nonconstant positive solutions. Moreover the author considers the bifurcation and the global existence with respect to diffusion terms of nonconstant positive solutions. The analysis of the author shows that the cross-diffusions may be source for the stationary patterns.
scientific article; zbMATH DE number 2082187
scientific article