Year: 2014
Type: preprint
Abstract: We study the convective wave equation in two space dimension driven by spatially homogeneous Gaussian noise. The existence of the real-valued solution is proved by providing a necessary and sufficient condition of Gaussian noise source. Our approach is based on the mild solution of the convective wave equation which is constructed by Walsh's theory of martingale measures. Hölder continuity of the solution is proved by using Green's function and Kolmogorov continuity theorem.
Source: arXiv (Cornell University)
Authors: Park, Sang-Hyeon, Sim, Imbo
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1596600719