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Winter 2010 Weak nonmild solutions to some SPDEs
Daniel Conus, Davar Khoshnevisan
Illinois J. Math. 54(4): 1329-1341 (Winter 2010). DOI: 10.1215/ijm/1348505531

Abstract

We study the nonlinear stochastic heat equation driven by space–time white noise in the case that the initial datum $u_0$ is a (possibly signed) measure. In this case, one cannot obtain a mild random-field solution in the usual sense. We prove instead that it is possible to establish the existence and uniqueness of a weak solution with values in a suitable function space. Our approach is based on a construction of a generalized stochastic convolution via Young-type inequalities.

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Daniel Conus. Davar Khoshnevisan. "Weak nonmild solutions to some SPDEs." Illinois J. Math. 54 (4) 1329 - 1341, Winter 2010. https://doi.org/10.1215/ijm/1348505531

Information

Published: Winter 2010
First available in Project Euclid: 24 September 2012

zbMATH: 1259.60067
MathSciNet: MR2981850
Digital Object Identifier: 10.1215/ijm/1348505531

Subjects:
Primary: 60H15
Secondary: 35R60

Rights: Copyright © 2010 University of Illinois at Urbana-Champaign

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Vol.54 • No. 4 • Winter 2010
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