Instability of Turing type for a reaction-diffusion system with unilateral obstacles modeled by variational inequalities

Väth, Martin

doi:10.21136/mb.2014.143849

Cited by 5 publications

(1 citation statement)

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“…The proof is based on an instability criterion for variational inequalities and a rather general formula relating the fixed point index of the flow of the obstacle problem with the topological degree of a certain associated operator [47]. For specific examples see [47,69].…”

Section: Stability Instability and Obstaclesmentioning

confidence: 99%

Global Dynamics, Blow-Up, and Bianchi Cosmology

Ben-Gal,

Brehm,

Buchner

et al. 2016

Preprint

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Many central problems in geometry, topology, and mathematical physics lead to questions concerning the long-time dynamics of solutions to ordinary and partial differential equations. Examples range from the Einstein field equations of general relativity to quasilinear reaction-advection-diffusion equations of parabolic type. Specific questions concern the convergence to equilibria, the existence of periodic, homoclinic, and heteroclinic solutions, and the existence and geometric structure of global attractors. On the other hand, many solutions develop singularities in finite time. The singularities have to be analyzed in detail before attempting to extend solutions beyond their singularities, or to understand their geometry in conjunction with globally bounded solutions. In this context we have also aimed at global qualitative descriptions of blow-up and grow-up phenomena.We survey some of our results supported in the framework of the Sonderforschungsbereich 647 "Space -Time -Matter" of the Deutsche Forschungsgemeinschaft.

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Section: Stability Instability and Obstaclesmentioning

confidence: 99%