Global Existence and Uniform Boundedness of Smooth Solutions to a Cross-Diffusion System with Equal Diffusion Rates |
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| Authors: | Yuan Lou Michael Winkler |
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| Institution: | 1. Institute for Mathematical Sciences, Renmin University of China, Beijing, China;2. Department of Mathematics, Ohio State University, Columbus, Ohio, USAlou@math.ohio-state.edu;4. Institut für Mathematik, Universit?t Paderborn, Paderborn, Germany |
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| Abstract: | We consider the Shigesada-Kawasaki-Teramoto cross-diffusion model for two competing species. If both species have the same random diffusion coefficients and the space dimension is less than or equal to three, we establish the global existence and uniform boundedness of smooth solutions to the model in convex domains. This extends some previous works of Kim 12 Kim, J.U. (1984). Smooth solutions to a quasilinear system of diffusion equations for a certain population model. Nonlinear Anal. 8:1121–1144.Crossref], Web of Science ®] , Google Scholar]] and Shim 21 Shim, S.-A. (2002). Uniform boundedness and convergence of solutions to cross-diffusion systems. J. Diff. Eqs. 185:281–305.Crossref], Web of Science ®] , Google Scholar]] in one dimensional space. |
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| Keywords: | Cross diffusion system Global existence Smooth solution Uniform boundedness |
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