A stability index for steady state solutions of boundary value problems for parabolic systems
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This article is published in Journal of Differential Equations.The article was published on 1991-06-01 and is currently open access. It has received 62 citations till now. The article focuses on the topics: Boundary value problem & Steady state (electronics).read more
Citations
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Journal ArticleDOI
Pointwise Semigroup Methods and Stability of Viscous Shock Waves
Kevin Zumbrun,Peter Howard +1 more
TL;DR: In this paper, it was shown that stability is determined by the simple and numerically computable condition that the number of zeroes of the Evans function in the right complex half-plane be equal to the dimension of the stationary manifold of nearby traveling wave solutions.
Journal ArticleDOI
Absolute and convective instabilities of waves on unbounded and large bounded domains
Björn Sandstede,Arnd Scheel +1 more
TL;DR: In this paper, the authors compare the spectra of the linearized evolution operators on unbounded and bounded domains for two classes of boundary conditions, namely, separated boundary conditions and periodic boundary conditions.
Book ChapterDOI
Stability of Large-Amplitude Shock Waves of Compressible Navier–Stokes Equations
TL;DR: In this article, the necessary and sufficient conditions for linearized and nonlinear planar viscous stability were established in one dimension and separated in multidimensions by a co-dimension one set, that both extend and sharpen the formal conditions of structural and dynamical stability found in classical physical literature.
Journal ArticleDOI
Errata to: 'Pointwise semigroup methods and stability of viscous shock waves'
Kevin Zumbrun,Peter Howard +1 more
TL;DR: In this article, a pointwise semigroup approach was proposed to analyze the stability of viscous wave systems in the context of ODE on L. The analysis is based on the gap lemma of the Evans function.
Journal ArticleDOI
Pointwise Green Function Bounds for Shock Profiles of Systems with Real Viscosity
Corrado Mascia,Kevin Zumbrun +1 more
TL;DR: In this paper, pointwise Green function bounds and linearized stability for viscous shock profiles of general hyperbolic-parabolic systems of conservation laws of dissipative type were established.
References
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Book
Methods of Bifurcation Theory
Shui-Nee Chow,Jack K. Hale +1 more
TL;DR: In this paper, the static and dynamic aspects of bifurcation theory, which are of particular pertinence to differential equations, have been discussed, and a discussion of the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied.
Journal ArticleDOI
A topological invariant arising in the stability analysis of travelling waves
TL;DR: In this paper, a traveling wave is characterized by its time invariant profile and its ability to translate at constant speed in a single spatial dimension, i.e., it is stable relative to perturbations in the initial conditions for solutions of partial differential equations.
Journal ArticleDOI
Stability of the travelling wave solution of the FitzHugh-Nagumo system
TL;DR: On demontre la stabilite relative au systeme complet d'equations aux derivees partielles de ces ondes de propagation as discussed by the authors, a.k.a.
Journal ArticleDOI
Large time behavior of solutions of systems of nonlinear reaction-diffusion equations*
TL;DR: In this article, the authors studied the asymptotic behavior of weakly coupled parabolic equations describing systems undergoing diffusion, convection and nonlinear interaction in a bounded spatial domain, and they showed that every solution with initial values in ε$ and subject to homogeneous Neumann boundary conditions decays exponentially to a spatially homogeneous function of time.
Related Papers (5)
The gap lemma and geometric criteria for instability of viscous shock profiles
Robert A. Gardner,Kevin Zumbrun +1 more