Mathematics – Probability
Scientific paper
2010-04-16
Mathematics
Probability
17 pages
Scientific paper
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 definition of a stochastic convolution via Young-type inequalities.
Conus Daniel
Khoshnevisan Davar
No associations
LandOfFree
Weak nonmild solutions to some SPDEs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Weak nonmild solutions to some SPDEs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak nonmild solutions to some SPDEs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-622933