Illinois Journal of Mathematics

Weak nonmild solutions to some SPDEs

Daniel Conus and Davar Khoshnevisan

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

First available in Project Euclid: 24 September 2012

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Zentralblatt MATH identifier

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


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

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