Heteroclinic connections of stationary solutions of scalar reaction-diffusion equations
P. Brunovský, B. Fiedler (1987)
Banach Center Publications
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P. Brunovský, B. Fiedler (1987)
Banach Center Publications
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Rybář, Vojtěch, Vejchodský, Tomáš
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We study systems of two nonlinear reaction-diffusion partial differential equations undergoing diffusion driven instability. Such systems may have spatially inhomogeneous stationary solutions called Turing patterns. These solutions are typically non-unique and it is not clear how many of them exists. Since there are no analytical results available, we look for the number of distinct stationary solutions numerically. As a typical example, we investigate the reaction-diffusion system designed...
Marek Fila (1987)
Banach Center Publications
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Philippe Laurençot (2004)
Banach Center Publications
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The existence of a one-parameter family of stationary solutions to a fragmentation equation with size diffusion is established. The proof combines a fixed point argument and compactness techniques.
Wei-Ming Ni (2004)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We discuss the stability and instability properties of steady state solutions to single equations, shadow systems, as well as systems. Our basic observation is that the more complicated the pattern are, the more unstable they tend to be.
Waniewski, Jacek (2007)
Computational & Mathematical Methods in Medicine
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Lobanov, A.I., Starozhilova, T.K., Chernyaev, A.P. (2001)
Discrete Dynamics in Nature and Society
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Gonzalo Galiano, Mark Adriaan Peletier (1998)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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