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APPROXIMATING DYNAMICS OF A SINGULARLY PERTURBED STOCHASTIC WAVE EQUATION WITH A RANDOM DYNAMICAL BOUNDARY CONDITION.
- Source :
- SIAM Journal on Mathematical Analysis; 2013, Vol. 45 Issue 5, p2790-2814, 25p
- Publication Year :
- 2013
-
Abstract
- This work is concerned with a singularly perturbed stochastic nonlinear wave equation with a random dynamical boundary condition. A splitting is used to establish the approximating equation of the system for a sufficiently small singular perturbation parameter. The approximating equation is a stochastic parabolic equation when the power exponent of the singular perturbation parameter is in [1/2, 1) but is a deterministic wave equation when the power exponent is in (1,+∞). Moreover, if the power exponent of a singular perturbation parameter is bigger than or equal to 1/2, the same limiting equation of the system is derived in the sense of distribution, as the perturbation parameter tends to zero. This limiting equation is a deterministic parabolic equation. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00361410
- Volume :
- 45
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- SIAM Journal on Mathematical Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 108648569
- Full Text :
- https://doi.org/10.1137/12088968X