Stability of Gasless Combustion Fronts in One-Dimensional Solids

@article{Ghazaryan2010StabilityOG,
  title={Stability of Gasless Combustion Fronts in One-Dimensional Solids},
  author={Anna Ghazaryan and Yuri Latushkin and Stephen Schecter and Aparecido J. de Souza},
  journal={Archive for Rational Mechanics and Analysis},
  year={2010},
  volume={198},
  pages={981-1030}
}
For gasless combustion in a one-dimensional solid, we show a type of nonlinear stability of the physical combustion front: if a perturbation of the front is small in both a spatially uniform norm and an exponentially weighted norm, then the perturbation stays small in the spatially uniform norm and decays in the exponentially weighted norm, provided the linearized operator has no eigenvalues in the right half-plane other than zero. Using the Evans function, we show that the zero eigenvalue must… 
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