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exponential weights

Mathematical Modelling of Natural Phenomena (1)

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Stability of Traveling Waves in Partly ParabolicSystems
A. Ghazaryan, Y. Latushkin, S. Schecter
Journal:

Mathematical Modelling of Natural Phenomena / Volume 8 / Issue 5 / 2013

Published online by Cambridge University Press:

17 September 2013, pp. 31-47

Print publication:

2013
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We review recent results on stability of traveling waves in partly parabolicreaction-diffusion systems with stable or marginally stable equilibria. We explain howattention to what are apparently mathematical technicalities has led to theorems thatallow one to convert spectral calculations, which are used in the sciences and engineeringto study stability of a wave, into detailed, theoretically-based information about thebehavior of perturbations of the wave.