Uniform boundedness and convergence of solutions to the systems with cross-diffusions dominated by self-diffusions
The author proves the uniform boundedness and convergence of global solution for quasilinear parabolic systems with cross-diffusions dominated by self-diffusions in population dynamics. Applying Gagliardo-Nirenberg type inequalities, some uniform \(W_2^1\)-bounds uniform in time are established. Convergence of solutions is established for systems with large diffusion coefficients.
scientific article; zbMATH DE number 1880145