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dc.contributor.authorSalins, M.en_US
dc.date.accessioned2021-08-03T13:01:15Z
dc.date.available2021-08-03T13:01:15Z
dc.date.issued2020
dc.identifier.citationM. Salins. "Existence and uniqueness for the mild solution of the stochastic heat equation with non-Lipschitz drift on an unbounded spatial domain." Stochastics and Partial Differential Equations: Analysis and Computations, https://doi.org/10.1007/s40072-020-00182-7
dc.identifier.issn2194-0401
dc.identifier.issn2194-041X
dc.identifier.urihttps://hdl.handle.net/2144/42826
dc.description.abstractWe prove the existence and uniqueness of the mild solution for a nonlinear stochastic heat equation defined on an unbounded spatial domain. The nonlinearity is not assumed to be globally, or even locally, Lipschitz continuous. Instead the nonlinearity is assumed to satisfy a one-sided Lipschitz condition. First, a strengthened version of the Kolmogorov continuity theorem is introduced to prove that the stochastic convolutions of the fundamental solution of the heat equation and a spatially homogeneous noise grow no faster than polynomially. Second, a deterministic mapping that maps the stochastic convolution to the solution of the stochastic heat equation is proven to be Lipschitz continuous on polynomially weighted spaces of continuous functions. These two ingredients enable the formulation of a Picard iteration scheme to prove the existence and uniqueness of the mild solution.en_US
dc.languageen
dc.language.isoen_US
dc.publisherSpringer Science and Business Media LLCen_US
dc.relation.ispartofStochastics and Partial Differential Equations: Analysis and Computations
dc.subjectMathematics and statisticsen_US
dc.titleExistence and uniqueness for the mild solution of the stochastic heat equation with non-Lipschitz drift on an unbounded spatial domainen_US
dc.typeArticleen_US
dc.description.versionAccepted manuscripten_US
dc.identifier.doi10.1007/s40072-020-00182-7
pubs.elements-sourcecrossrefen_US
pubs.notesEmbargo: Not knownen_US
pubs.organisational-groupBoston Universityen_US
pubs.organisational-groupBoston University, College of Arts & Sciencesen_US
pubs.organisational-groupBoston University, College of Arts & Sciences, Department of Mathematics & Statisticsen_US
pubs.publication-statusPublished onlineen_US
dc.date.online2020-09-10
dc.identifier.mycv539309


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