Uniform boundedness and convergence of solutions to cross-diffusion systems

[摘要] Uniform boundedness and convergence of global solutions are proved for cross-diffusion systems in Population dynamics. Gagliardo-Nirenberg type inequalities are used in the estimates of solutions in order to establish W-2(1)-bounds uniform in time. In each step of estimates the contribution of the diffusion coefficients are emphasized, and it is concluded that the uniform bound remains independent of the growth of the diffusion coefficient in the system. Hence convergence of solutions are established for systems with large diffusion coefficients. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-10-10

[关键词] cross-diffusion system;uniform bound;convergence