Abstract
In this paper, we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion processes. In particular, we discuss the exit problem and metastability for the processes corresponding to quasi-linear initial-boundary value problems.
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Freidlin, M., Koralov, L. Nonlinear stochastic perturbations of dynamical systems and quasi-linear parabolic PDE’s with a small parameter. Probab. Theory Relat. Fields 147, 273–301 (2010). https://doi.org/10.1007/s00440-009-0208-8
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DOI: https://doi.org/10.1007/s00440-009-0208-8
Keywords
- Nonlinear perturbations
- Exit problem
- Metastability
Mathematics Subject Classification (2000)
- 60F10
- 35K55