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

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  • 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.
    Mathematics Subject Classification: Primary: 35K57, 35K50; Secondary: 35B35.


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