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Zbl 1157.35054
Yamauchi, Yusuke
Blow-up results for a reaction-diffusion system. (English)
[J] Methods Appl. Anal. 13, No. 4, 337-349 (2006). ISSN 1073-2772

The author considered the Cauchy problem for the reaction-diffusion system with the nonlinear terms $|x|^{\sigma_j}u^{p_j}v^{q_j}$. It is shown that the exponents $p_j , q_j , \sigma_j$ play a crucial role to determine the behavior of the solutions. Using an ODE method, the author proved the Fujita-type nonexistence results for $p_1, q_2<1$, for $q_2<1<p_1$ or for $p_1, q_2>1$. In addition, the author also showed the nonexistence results for large initial data.
[Pigong Han (Beijing, China)]

MSC 2000:: *35K45 Systems of parabolic equations, initial value problems
35B33 Critical exponents
35B40 Asymptotic behavior of solutions of PDE
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations
35B05 General behavior of solutions of PDE

Keywords: blow-up; reaction-diffusion system; Cauchy problem; Fujita-type nonexistence results; nonexistence results for large initial data

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Zentralblatt MATH Berlin [Germany]