科研之友
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摘要
We consider the stochastic heat equation of the form partial derivative u/partial derivative t = (triangle + triangle(alpha))u + (partial derivative f/partial derivative x)(t, x, u) + o(t, x, u) L + W-H, where W-H is the fractional noise, L is a (pure jump) Levy space-time white noise, triangle is Laplacian, and triangle(alpha) = -(-triangle)(alpha/2) is the fractional Laplacian generator on R, and f, sigma : [ 0, T] x R x R -> R are measurable functions. We introduce the existence and uniqueness of the solution by the fixed point principle under some suitable assumptions.
