Eigenvalues of inequalities of reaction-diffusion type and destabilizing effect of unilateral conditions (original) (raw)

Czechoslovak Mathematical Journal

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A priori bounds for reaction-diffusion systems arising in chemical and biological dynamics

Applied Mathematics and Computation, 2005

The authors investigate reaction-diffusion equations which arise in chemical and biological dynamics. It is shown that several common systems share a useful property, a structure on the non-linearity which arises from conservation of mass or population. This conservation property is used to demonstrate a priori bounds for the parabolic problems and the associated elliptic problem. The types of systems included in the analysis are the Gray-Scott system, SIR model, and the Selkov model of glycolysis.

Global bifurcation for quasivariational inequalities of reaction–diffusion type

Journal of Mathematical Analysis and Applications, 2008

We consider a reaction-diffusion system with implicit unilateral boundary conditions introduced by U. Mosco. We show that global continua of stationary spatially nonhomogeneous solutions bifurcate in the domain of parameters where bifurcation in the case of classical boundary conditions is excluded. The problem is formulated as a quasivariational inequality and the proof is based on the Leray-Schauder degree.

Diffusion-Driven Instability in Reaction᎐Diffusion Systems

For a stable matrix A with real entries, sufficient and necessary conditions for A y D to be stable for all non-negative diagonal matrices D are obtained. Implications of these conditions for the stability and instability of constant steadystate solutions to reaction᎐diffusion systems are discussed and an example is given to show applications. ᮊ

Instabilities in reaction-diffusion systems

Applied mathematical sciences, 2014

In this paper we discuss the solution stability of two-component reaction-diffusion systems with constant diffusion coefficients. Linear stability analysis is performed near the steady state solution of the system discussing the dependence of the system stability on its parameters. A comprehensive linear stability analysis results in three types of instabilities: (1) Stationary periodic, (2) Oscillatory uniform and (3) Stationary uniform. Precise parameter regimes are identified for each. Mathematics Subject Classification: 35B36, 35K57, 70K50

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