Abstract
Uniform boundedness and convergence of global solutions are proved for quasilinear parabolic systems with a single nonzero cross-diffusion in population dynamics. Gagliardo–Nirenberg type inequalities are used in the estimates of solutions in order to establish W 1 2-bounds uniform in time. By using the uniform bound, convergence of solutions are established for systems with large diffusion coefficients in the weak competition case.
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