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

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

2010-05-20

arxiv.org/abs/1005.3804v1

C. R. Math. Acad. Sci. Paris 336 (2003), no. 4, 309-314

Mathematics

Analysis of PDEs

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

Scientific paper

10.1016/S1631-073X(03)00060-8

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 $\scriptstyle d$-dimensional space: $\scriptstyle{\eight{u_t=-\frac18\Delta^2u-\frac12\Delta u-\frac12u}}$. The solution is given in terms of a functional of our LKSP.

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