Displaying similar documents to “Global existence and convergence to steady states in a chemorepulsion system”

Lyapunov Functions for Weak Solutions of Reaction-Diffusion Equations with Discontinuous Interaction Functions and its Applications

Mark O. Gluzman, Nataliia V. Gorban, Pavlo O. Kasyanov (2015)

Nonautonomous Dynamical Systems

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In this paper we investigate additional regularity properties for global and trajectory attractors of all globally defined weak solutions of semi-linear parabolic differential reaction-diffusion equations with discontinuous nonlinearities, when initial data uτ ∈ L2(Ω). The main contributions in this paper are: (i) sufficient conditions for the existence of a Lyapunov function for all weak solutions of autonomous differential reaction-diffusion equations with discontinuous and multivalued...

Convergence and stability of higher-order finite element solution of reaction-diffusion equation with Turing instability

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.

The quasineutral limit problem in semiconductors sciences

Ling Hsiao (2004)

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

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The mathematical analysis on various mathematical models arisen in semiconductor science has attracted a lot of attention in both applied mathematics and semiconductor physics. It is important to understand the relations between the various models which are different kind of nonlinear system of P.D.Es. The emphasis of this paper is on the relation between the drift-diffusion model and the diffusion equation. This is given by a quasineutral limit from the DD model to the diffusion equation. ...

Behaviour of global solutions for a system of reaction-diffusion equations from combustion theory

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.

Hypocoercive Diffusion Operators

Cédric Villani (2007)

Bollettino dell'Unione Matematica Italiana

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In many problems coming from mathematical physics, the association of a degenerate diffusion operator with a conservative operator may lead to dissipation in all variables and convergence to equilibrium. One can draw an analogy with the well-studied phenomenon of hypoellipticity in regularity theory, and actually both phenomena have been studied together. Now a distinctive theory of ``hypocoercivity'' is starting to emerge, with already some striking results, and several challenging...