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: $\scriptstyle{\eight{u_t=-\frac18Δ^2u-\frac12Δu-\frac12u}}$. The solution is given in terms of a functional of our LKSP.

5 pages, 6/9 papers from my 2000-2006 collection (preprint version)

References in corpus (3)

• Brownian-Time Processes: The PDE Connection and the Half-Derivative Generator
• Brownian-Time Processes: The PDE Connection II and the Corresponding Feynman-Kac Formula
• A linearized Kuramoto-Sivashinsky PDE via an imaginary-Brownian-time-Brownian-angle process

Cited by in corpus (1)

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