Uniform Boundedness and Convergence of Solutions to Cross-Diffusion Systems

By Seong-a Shim. 2002

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The boundedness-by-entropy principle for cross-diffusion systems (2014, background): “In fact, in one space dimension and with coefficients α10 = α20, Shim [55] proved uniform upper bounds.”
On global existence of solutions to a cross-diffusion system (2008, unknown): “1”
Diffusive and nondiffusive population models (2010, background): “the convergence to the steady states as t → ∞ [133, 134, 135, 136].”
The boundedness-by-entropy method for cross-diffusion systems (2015, background): “In fact, in one space dimension and with coefficients α10 = α20, Shim [60] proved uniform upper bounds.”
Global Existence and Uniform Boundedness of Smooth Solutions to a Cross-Diffusion System with Equal Diffusion Rates (2015, methodology): “Later on Shim [21] proved the uniform boundedness of smooth solutions when n = 1 and d1 = d2.”