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dc.contributor.authorAllouba, Hassan ( )
dc.date.accessioned2021-01-28T19:52:09Z
dc.date.available2021-01-28T19:52:09Z
dc.date.issued2003-11-05
dc.identifier.citationAllouba, H. (2003). SDDEs limits solutions to sublinear reaction-diffusion SPDEs. Electronic Journal of Differential Equations, 2003(111), pp. 1-21.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13162
dc.description.abstractWe 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.en_US
dc.formatText
dc.format.extent21 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectReaction-diffusion SPDEen_US
dc.subjectSDDEen_US
dc.subjectSDDE limits solutionsen_US
dc.subjectMultiscaleen_US
dc.titleSDDEs limits solutions to sublinear reaction-diffusion SPDEsen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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