Blow-up Results for a Reaction-Diffusion System

• Autores: Yusuke Yamauchi
• Localización: Methods and applications of analysis, ISSN 1073-2772, Vol. 13, Nº 4, 2006, págs. 337-350
• Idioma: inglés
• DOI: 10.4310/maa.2006.v13.n4.a2
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• Resumen

  • We consider the Cauchy problem for the reaction-diffusion system with the nonlinear terms |x| jupj vqj . In this system, the exponents p1 and q2 play a crucial role to determine the behavior of the solutions. Using an ODE method, we prove the Fujita-type nonexistence results for p1, q2 < 1, for q2 < 1 < p1 or for p1, q2 > 1. Moreover, we also show the nonexistence results for large initial data.