Global existence from single-component 𝐿_{𝑝} estimates in a semilinear reaction-diffusion system

Quittner, Pavol; Souplet, Philippe

doi:10.1090/S0002-9939-02-06453-5

Global existence from single-component $L_{p}$ estimates in a semilinear reaction-diffusion system
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by Pavol Quittner and Philippe Souplet PDF

Proc. Amer. Math. Soc. 130 (2002), 2719-2724 Request permission

Abstract:

For a system of two reaction-diffusion equations coupled by power nonlinearities, we prove that an $L_{p}$ bound on a single component for suitable $p$ is enough to guarantee global existence. Also we provide a strong indication that our condition on $p$ is the best possible. Moreover, this continuation result is in contrast with the corresponding necessary and sufficient conditions for local existence obtained earlier by the authors.

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