A Modulus for the 3-Dimensional Wave Equation With Noise: Dealing With a Singular Kernel
Carl Mueller · Canadian Journal of Mathematics · 1993
Abstract We give a modulus of continuity for solutions of the wave equation with a noise term: utt = Δu + a(u) + b(u)G, x ∈ ℝ3 where G is a Gaussian noise. This case is more difficult than in lower dimensions because the fundamental solution of the wave equation is singular.