Stochastic Perturbations of the Allen-Cahn Equation
| dc.contributor.author | Shardlow, Tony | |
| dc.date.accessioned | 2020-01-07T16:08:19Z | |
| dc.date.available | 2020-01-07T16:08:19Z | |
| dc.date.issued | 2000-06-15 | |
| dc.description.abstract | Consider the Allen-Cahn equation with small diffusion ∈² perturbed by a space time white noise of intensity σ. In the limit, σ/∈² → 0, solutions converge to the noise free problem in the L² norm. Under these conditions, asymptotic results for the evolution of phase boundaries in the deterministic setting are extended, to describe the behaviour of the stochastic Allen-Cahn PDE by a system of stochastic differential equations. Computations are described, which support the asymptotic derivation. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 19 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Shardlow, T. (2000). Stochastic perturbations of the Allen-Cahn equation. <i>Electronic Journal of Differential Equations, 2000</i>(47), pp. 1-19. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/9141 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2000, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Dynamics of phase-boundaries | |
| dc.subject | Stochastic partial differential equations | |
| dc.subject | Asymptotics | |
| dc.title | Stochastic Perturbations of the Allen-Cahn Equation | |
| dc.type | Article |