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Zbl 1050.35031
Kobayashi, Yasumaro
Behavior of the life span for solutions to the system of reaction-diffusion equations.
(English)
[J] Hiroshima Math. J. 33, No. 2, 167-187 (2003). ISSN 0018-2079

The author studies the following reaction-diffusion systems $$\partial_t u=\Delta u+a(x)v^p, \quad\partial_t v=\Delta v+b(x)u^q$$ in the total space $\bbfR^N.$ Conditions for the existence, blow-up and global existence of solutions to the above systems in terms of the growth as $x\to\infty$ of the functions $a(x),b(x)$ and the initial data $u_0,v_0$ are given.
[Sen-Zhong Huang (Hamburg)]
MSC 2000:
*35K45 Systems of parabolic equations, initial value problems
35B05 General behavior of solutions of PDE
35K57 Reaction-diffusion equations

Keywords: existence; blow-up

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