Illinois Journal of Mathematics

Weak nonmild solutions to some SPDEs

Daniel Conus and Davar Khoshnevisan

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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.

Article information

Source
Illinois J. Math., Volume 54, Number 4 (2010), 1329-1341.

Dates
First available in Project Euclid: 24 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1348505531

Digital Object Identifier
doi:10.1215/ijm/1348505531

Mathematical Reviews number (MathSciNet)
MR2981850

Zentralblatt MATH identifier
1259.60067

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]

Citation

Conus, Daniel; Khoshnevisan, Davar. Weak nonmild solutions to some SPDEs. Illinois J. Math. 54 (2010), no. 4, 1329--1341. doi:10.1215/ijm/1348505531. https://projecteuclid.org/euclid.ijm/1348505531


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