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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.22 No.1

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Global solutions of the cooperative cross-fiffusion systems

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2015, v.22 no.1, pp.75-90
https://doi.org/10.7468/jksmeb.2015.22.1.75
Shim, Seong-A
Shim,, S. (2015). Global solutions of the cooperative cross-fiffusion systems. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 22(1), 75-90, https://doi.org/10.7468/jksmeb.2015.22.1.75

Abstract

In this paper the existence of global solutions of the parabolic cross-diffusion systems with cooperative reactions is obtained under certain conditions. The uniform boundedness of <TEX>$W_{1,2}$</TEX> norms of the local maximal solution is obtained by using interpolation inequalities and comparison results on differential inequalities.

keywords
cross-diffusion systems, cooperative dynamics, existence of global solutions, uniform bound

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Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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