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2005 Coexistence of simultaneous and nonsimultaneous blow-up in a semilinear parabolic system
Julio D. Rossi, Philippe Souplet
Differential Integral Equations 18(4): 405-418 (2005).

Abstract

We study simultaneous and nonsimultaneous blow-up for solutions of the following system $$\left\{\begin{array}{l} u_t = \Delta u + u^r + v^p, \\ v_t = \Delta v + v^s + u^q, \end{array} \quad\mbox{ in } \Omega \times (0,T), \right. $$ with Dirichlet boundary conditions. We show that, in the range of exponents where either component may blow up alone, there also exist initial data for which both components blow up simultaneously. The proof is based on a continuity argument, which requires upper and lower blow-up estimates, independent of initial data, and continuous dependence of the existence time. In turn, we prove a result of continuous dependence of the existence time, under the assumption of uniform upper blow-up estimates, in the framework of general abstract semiflows.

Citation

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Julio D. Rossi. Philippe Souplet. "Coexistence of simultaneous and nonsimultaneous blow-up in a semilinear parabolic system." Differential Integral Equations 18 (4) 405 - 418, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35219
MathSciNet: MR2122706

Subjects:
Primary: 35K50
Secondary: 35B40 , 35K55

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 4 • 2005
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