Finite-point extinction and continuity of interfaces in a nonlinear diffusion equation with strong absorption.
X.-Y. Chen, Hiroshi Matano, M. Mimura (1995)
Journal für die reine und angewandte Mathematik
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X.-Y. Chen, Hiroshi Matano, M. Mimura (1995)
Journal für die reine und angewandte Mathematik
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Kůs, Pavel
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In this contribution, higher-order finite element method is used for the solution of reaction-diffusion equation with Turing instability. Some aspects concerning convergence of the method for this particular problem are discussed. Our numerical tests confirm the convergence of the method, but for some very special choices of parameters, this convergence has very uncommon properties.
F.A. Howes (1988)
Journal für die reine und angewandte Mathematik
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Peter Polácik (1989)
Journal für die reine und angewandte Mathematik
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Pavol Quittner (1987)
Journal für die reine und angewandte Mathematik
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Salah Badraoui (1999)
Applicationes Mathematicae
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We are concerned with the boundedness and large time behaviour of the solution for a system of reaction-diffusion equations modelling complex consecutive reactions on a bounded domain under homogeneous Neumann boundary conditions. Using the techniques of E. Conway, D. Hoff and J. Smoller [3] we also show that the bounded solution converges to a constant function as t → ∞. Finally, we investigate the rate of this convergence.
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.
Yuan-Ming Wang (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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This paper is concerned with the asymptotic behavior of the finite difference solutions of a class of nonlinear reaction diffusion equations with time delay. By introducing a pair of coupled upper and lower solutions, an existence result of the solution is given and an attractor of the solution is obtained without monotonicity assumptions on the nonlinear reaction function. This attractor is a sector between two coupled quasi-solutions of the corresponding “steady-state" problem,...
Liljana Stefanovska, Toma Grcev, Sonja Gegovska-Zajkova (2002)
Visual Mathematics
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A.K. Aziz, A.B. Stephens, Manil Suri (1988)
Numerische Mathematik
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Thomas Elsken (2004)
Studia Mathematica
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