Issoglio, E orcid.org/0000-0003-3035-2712 (2019) A non-linear parabolic PDE with a distributional coefficient and its applications to stochastic analysis. Journal of Differential Equations, 267 (10). pp. 5976-6003. ISSN 0022-0396
Abstract
We consider a non-linear parabolic partial differential equation (PDE) on with a distributional coefficient in the non-linear term. The distribution is an element of a Besov space with negative regularity and the non-linearity is of quadratic type in the gradient of the unknown. Under suitable conditions on the parameters we prove local existence and uniqueness of a mild solution to the PDE, and investigate properties like continuity with respect to the initial condition and blow-up times. We prove a global existence and uniqueness result assuming further properties on the non-linearity. To conclude we consider an application of the PDE to stochastic analysis, in particular to a class of non-linear backward stochastic differential equations with distributional drivers.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Elsevier Inc. All rights reserved. This is an author produced version of an article published in Journal of Differential Equations. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Distributional coefficients; Singular parabolic PDEs; Singular BSDEs; Quadratic parabolic PDEs; Besov spaces |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Jul 2019 08:23 |
Last Modified: | 26 Jun 2020 00:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jde.2019.06.014 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147757 |
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