A linearized Kuramoto–Sivashinsky PDE via an imaginary-Brownian-time-Brownian-angle process

Abstract

We introduce a new imaginary-Brownian-time-Brownian-angle process, which we also call the linear-Kuramoto–Sivashinsky process (LKSP). Building on our techniques in two recent articles involving the connection of Brownian-time processes to fourth order PDEs, we give an explicit solution to a linearized Kuramoto–Sivashinsky PDE in d-dimensional space: u t=− 1 8 Δ 2u− 1 2 Δu− 1 2 u . The solution is given in terms of a functional of our LKSP. To cite this article: H. Allouba, C. R. Acad. Sci. Paris, Ser. I 336 (2003).