SDDEs limits solutions to sublinear reaction-diffusion SPDEs
| dc.contributor.author | Allouba, Hassan | |
| dc.date.accessioned | 2021-01-28T19:52:09Z | |
| dc.date.available | 2021-01-28T19:52:09Z | |
| dc.date.issued | 2003-11-05 | |
| dc.description.abstract | We start by introducing a new definition of solutions to heat-based SPDEs driven by space-time white noise: SDDEs (stochastic differential-difference equations) limits solutions. In contrast to the standard direct definition of SPDEs solutions; this new notion, which builds on and refines our SDDEs approach to SPDEs from earlier work, is entirely based on the approximating SDDEs. It is applicable to, and gives a multiscale view of, a variety of SPDEs. We extend this approach in related work to other heat-based SPDEs (Burgers, Allen-Cahn, and others) and to the difficult case of SPDEs with multi-dimensional spacial variable. We focus here on one-spacial-dimensional reaction-diffusion SPDEs; and we prove the existence of a SDDEs limit solution to these equations under less-than-Lipschitz conditions on the drift and the diffusion coefficients, thus extending our earlier SDDEs work to the nonzero drift case. The regularity of this solution is obtained as a by-product of the existence estimates. The uniqueness in law of our SPDEs follows, for a large class of such drifts/diffusions, as a simple extension of our recent Allen-Cahn uniqueness result. We also examine briefly, through order parameters ∈1, ∈2 → 0 at different speeds. More precisely, it is shown that the ratio ∈2 / ∈1 1/4 determines the behavior as ∈1, ∈2 → 0. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 21 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Allouba, H. (2003). SDDEs limits solutions to sublinear reaction-diffusion SPDEs. <i>Electronic Journal of Differential Equations, 2003</i>(111), pp. 1-21. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13162 | |
| 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, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Reaction-diffusion SPDE | |
| dc.subject | SDDE | |
| dc.subject | SDDE limits solutions | |
| dc.subject | Multiscale | |
| dc.title | SDDEs limits solutions to sublinear reaction-diffusion SPDEs | |
| dc.type | Article |