Weak nonmild solutions to some SPDEs∗
نویسندگان
چکیده
We study the nonlinear stochastic heat equation driven by spacetime 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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تاریخ انتشار 2010