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A linearized Kuramoto-Sivashinsky PDE via an imaginary-Brownian-time-Brownian-angle process (1005.3804v1)
Published 20 May 2010 in math.AP, math-ph, math.CV, math.MP, and math.PR
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 $\scriptstyle d$-dimensional space: $\scriptstyle{\eight{u_t=-\frac18\Delta2u-\frac12\Delta u-\frac12u}}$. The solution is given in terms of a functional of our LKSP.
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