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January  2006, 14(1): 63-74. doi: 10.3934/dcds.2006.14.63

Dirichlet boundary conditions can prevent blow-up in reaction-diffusion equations and systems

Marek Fila 1, , Hirokazu Ninomiya 2, and  Juan-Luis Vázquez 3,

1. 

Department of Applied Mathematics and Statistics, Comenius University, 842 48 Bratislava, Slovak Republic
2. 

Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu 520-2194, Japan
3. 

Departamento de Matemáticas, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid

Received  October 2004 Revised  February 2005 Published  October 2005

This paper examines the following question: Suppose that we have a reaction-diffusion equation or system such that some solutions which are homogeneous in space blow up in finite time. Is it possible to inhibit the occurrence of blow-up as a consequence of imposing Dirichlet boundary conditions, or other effects where diffusion plays a role? We give examples of equations and systems where the answer is affirmative.
Keywords: Blow-up, reaction-diffusion, Dirichlet conditions prevent blow-up..
Mathematics Subject Classification: Primary: 35K57, 35K50; Secondary: 35B3.
Citation: Marek Fila, Hirokazu Ninomiya, Juan-Luis Vázquez. Dirichlet boundary conditions can prevent blow-up in reaction-diffusion equations and systems. Discrete and Continuous Dynamical Systems, 2006, 14 (1) : 63-74. doi: 10.3934/dcds.2006.14.63
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