Nonlinear stochastic wave and heat equations
We study nonlinear wave and heat equations on ℝ d driven by a spatially homogeneous Wiener process. For the wave equation we consider the cases of d = 1, 2, 3. The heat equation is considered on an arbitrary ℝ d -space. We give necessary and sufficient conditions for the existence of a function-valued solution in terms of the covariance kernel of the noise.
KeywordsCovariance Wave Equation Heat Equation Nonlinear Wave Wiener Process
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