The finite speed of propagation for solutions to nonlinear stochastic wave equations driven by multiplicative noise
We prove that the solutions to the stochastic wave equation in O subset of R-d, d(X) over dot - Delta X dt + g(X) dt = sigma(X)dW, for 1 <= d <= infinity, where g is a continuous function with polynomial growth of order less or equal to d/ d-2 and sigma is Lipschitz with sigma(0) = 0, propagate with finite speed. This result resembles the classical finite speed of propagation result for the solution to the Klein-Gordon equation and extends to equations with dissipative damping. A similar result follows for the equation with additive noise of the form F(t)dW, where F(t) = F(t, xi) has compact support (in xi) for each t > 0. (C) 2013 Elsevier Inc. All rights reserved.
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