Weak nonmild solutions to some SPDEs

2010/04/16 by Daniel Conus, Davar Khoshnevisan, Conus, Daniel +1
Mathematics · #FOS: Mathematics #Primary 60H15 #Probability (math.PR) #Secondary 35R60. #math.PR #msc:35R60. #msc:60H15

paper · pdf · doi:10.48550/arxiv.1004.2744

17 pages

arxiv created 2010/04/16 · arxiv updated 2010/04/19

Abstract

We study the nonlinear stochastic heat equation driven by space-time white noise in the case that the initial datum u₀ 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.

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