On a reaction diffusion problem with a moving impulse on boundary
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Alioune Coulibaly
Abstract
We study an asymptotic problem of a semilinear partial differential equation (PDE) with Neumann boundary condition, periodic coefficients and highly oscillating drift and nonlinear terms. Our analysis focuses on the double limiting behavior of the PDE-solution perturbed by ε (viscosity parameter) and δ (scaling coefficient) both tending to zero. To do so, we state basic properties of the large deviations principle (LDP) and we express the logarithmic asymptotic of the PDE-solution. Particularly, we provide it for the case when ε converges more quickly than δ.
Acknowledgements
The author thanks the referees and editor for their careful reading and helpful suggestions which lead to a much improved version of this paper.
References
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Articles in the same Issue
- Frontmatter
- On a reaction diffusion problem with a moving impulse on boundary
- Backward doubly stochastic differential equations driven by fractional Brownian motion with stochastic integral-Lipschitz coefficients
- Stochastic controls of fractional Brownian motion
- QMLE for periodic absolute value GARCH models
- The generalized canonical equations K 1, K 7, K 16, K 27. The REFORM method, the invariance principal method, the matrix expansion method and G-transform. The main stochastic canonical equations K 100,...,K 106 and the estimators G 55,...,G 58 of the MAGIC (Mathematical Analysis of General Invisible Components)
Articles in the same Issue
- Frontmatter
- On a reaction diffusion problem with a moving impulse on boundary
- Backward doubly stochastic differential equations driven by fractional Brownian motion with stochastic integral-Lipschitz coefficients
- Stochastic controls of fractional Brownian motion
- QMLE for periodic absolute value GARCH models
- The generalized canonical equations K 1, K 7, K 16, K 27. The REFORM method, the invariance principal method, the matrix expansion method and G-transform. The main stochastic canonical equations K 100,...,K 106 and the estimators G 55,...,G 58 of the MAGIC (Mathematical Analysis of General Invisible Components)
