Stochastic NonLinear Wave Equations in Local Sobolev Spaces

Martin Ondrejat (Academy of Sciences of the Czech Republic)

Abstract


Existence of weak solutions of stochastic wave equations with nonlinearities of a critical growth driven by spatially homogeneous Wiener processes is established in local Sobolev spaces and local energy estimates for these solutions are proved. A new method to construct weak solutions is employed.

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Pages: 1041-1091

Publication Date: July 6, 2010

DOI: 10.1214/EJP.v15-789

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