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Uniform boundedness and convergence of solutions to the systems with cross-diffusions dominated by self-diffusions. (English) Zbl 1015.35020

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.
Reviewer: S.Anita (Iaşi)

MSC:

35B45 A priori estimates in context of PDEs
35K57 Reaction-diffusion equations
92D25 Population dynamics (general)
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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