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On the reducibility of the \(L^{2}\)-stability of ternary reaction-diffusion systems of P.D.Es. (English) Zbl 1242.35043

Greco, A. M. (ed.) et al., Proceedings “WASCOM 2009”. 15th conference on waves and stability in continuous media, Palermo, Italy, June 28–July 1, 2009. Hackensack, NJ: World Scientific (ISBN 978-981-4317-41-2/hbk; 978-981-4317-42-9/ebook). 321 (2010).
Summary: The \(L^2\)-stability of nonlinear ternary reaction-diffusion systems of PDEs – under Robin boundary conditions – is considered. Conditions guaranteeing the reducibility of the \(L^2\)-stability to the stability of a ternary linear system of ODEs via the direct method are obtained.
For the entire collection see [Zbl 1237.35006].

MSC:

35B35 Stability in context of PDEs
35K57 Reaction-diffusion equations
35K51 Initial-boundary value problems for second-order parabolic systems
35K58 Semilinear parabolic equations
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