scholarly journals Balanced flux formulations for multidimensional Evans-function computations for viscous shocks

2017 ◽  
Vol 76 (3) ◽  
pp. 531-545 ◽  
Author(s):  
Blake Barker ◽  
Jeffrey Humpherys ◽  
Gregory Lyng ◽  
Kevin Zumbrun
Keyword(s):  
Evans Function

scholarly journals Stability analysis of combustion waves for competitive exothermic reactions using Evans function

2018 ◽  
Vol 54 ◽  
pp. 347-360 ◽  
Author(s):  
Z. Huang ◽  
H.S. Sidhu ◽  
I.N. Towers ◽  
Z. Jovanoski ◽  
V.V. Gubernov
Keyword(s):  
Stability Analysis ◽  
Evans Function ◽  
Combustion Waves ◽  
Exothermic Reactions

Evans function analysis of the stability of non-adiabatic flames

2003 ◽  
Vol 7 (3) ◽  
pp. 545-561 ◽  
Author(s):  
Peter L Simon ◽  
Serafim Kalliadasis ◽  
John H Merkin ◽  
Stephen K Scott
Keyword(s):  
Function Analysis ◽  
Evans Function ◽  
The Stability

A stability index for travelling waves in activator-inhibitor systems

2019 ◽  
Vol 150 (1) ◽  
pp. 517-548
Author(s):  
Paul Cornwell ◽  
Christopher K. R. T. Jones
Keyword(s):  
Eigenvalue Problem ◽  
Symplectic Form ◽  
Travelling Waves ◽  
Stability Index ◽  
Maslov Index ◽  
Evans Function ◽  
Conjugate Points ◽  
Spatial Evolution ◽  
The Stability ◽  
Activator Inhibitor

AbstractWe consider the stability of nonlinear travelling waves in a class of activator-inhibitor systems. The eigenvalue equation arising from linearizing about the wave is seen to preserve the manifold of Lagrangian planes for a nonstandard symplectic form. This allows us to define a Maslov index for the wave corresponding to the spatial evolution of the unstable bundle. We formulate the Evans function for the eigenvalue problem and show that the parity of the Maslov index determines the sign of the derivative of the Evans function at the origin. The connection between the Evans function and the Maslov index is established by a ‘detection form,’ which identifies conjugate points for the curve of Lagrangian planes.

scholarly journals The Evans function for nonlocal equations

2004 ◽  
Vol 53 (4) ◽  
pp. 1095-1126 ◽  
Author(s):  
Todd Kapitula ◽  
Nathan Kutz ◽  
Bjorn Sandstede
Keyword(s):  
Evans Function ◽  
Nonlocal Equations

EVANS FUNCTIONS AND NONLINEAR STABILITY OF TRAVELING WAVES IN NEURONAL NETWORK MODELS

2007 ◽  
Vol 17 (08) ◽  
pp. 2693-2704 ◽  
Author(s):  
BJÖRN SANDSTEDE
Keyword(s):  
Differential Equations ◽  
Neuronal Network ◽  
Nonlinear Stability ◽  
Traveling Waves ◽  
Network Models ◽  
Function Spaces ◽  
Spectral Stability ◽  
Evans Function ◽  
Evans Functions

Modeling networks of synaptically coupled neurons often leads to systems of integro-differential equations. Particularly interesting solutions in this context are traveling waves. We prove here that spectral stability of traveling waves implies their nonlinear stability in appropriate function spaces, and compare several recent Evans-function constructions that are useful tools when analyzing spectral stability.

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