Displaying similar documents to “ L 2 -stability of the solutions to a nonlinear binary reaction-diffusion system of P.D.E.s”

Convective Instability of Reaction Fronts in Porous Media

K. Allali, A. Ducrot, A. Taik, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

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We study the influence of natural convection on stability of reaction fronts in porous media. The model consists of the heat equation, of the equation for the depth of conversion and of the equations of motion under the Darcy law. Linear stability analysis of the problem is fulfilled, the stability boundary is found. Direct numerical simulations are performed and compared with the linear stability analysis.

Unconditional nonlinear exponential stability in the Bénard problem for a mixture: necessary and sufficient conditions

Giuseppe Mulone, Salvatore Rionero (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The Lyapunov direct method is applied to study nonlinear exponential stability of a basic motionless state to imposed linear temperature and concentration fields of a binary fluid mixture heated and salted from below, in the Oberbeck-Boussinesq scheme. Stress-free and rigid surfaces are considered and absence of Hopf bifurcation is assumed. We prove the coincidence of the linear and (unconditional) nonlinear critical stability limits, when the ratio between the Schmidt and the Prandtl...

Stability analysis of phase boundary motion by surface diffusion with triple junction

Harald Garcke, Kazuo Ito, Yoshihito Kohsaka (2009)

Banach Center Publications

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The linearized stability of stationary solutions for the surface diffusion flow with a triple junction is studied. We derive the second variation of the energy functional under the constraint that the enclosed areas are preserved and show a linearized stability criterion with the help of the H - 1 -gradient flow structure of the evolution problem and the analysis of eigenvalues of a corresponding differential operator.