Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 54, Number 4 (2010), 1329-1341.
Weak nonmild solutions to some SPDEs
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.
Illinois J. Math., Volume 54, Number 4 (2010), 1329-1341.
First available in Project Euclid: 24 September 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.ijm/1348505531