Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1231.35016
Arioli, Gianni; Koch, Hans
Computer-assisted methods for the study of stationary solutions in dissipative systems, applied to the Kuramoto-Sivashinski equation. (English)
[J] Arch. Ration. Mech. Anal. 197, No. 3, 1033-1051 (2010). ISSN 0003-9527; ISSN 1432-0673/e

The authors develop computer-assisted techniques for the analysis of stationary solutions, of stability, and of bifurcation diagrams of parabolic equations of the form $\partial_t u + (i\partial_x)^m u+H_{\alpha} (u, \partial_x u, \dots, \partial_x^{m-1} u)=0$ with even positive $m$, $H_{\alpha}$ real analytic, and $u(x,t)$ periodic in $x$. As a case of study, these methods are applied to the Kuramoto-Sivashinski equation. The authors rigorously describe the full graph of solutions branching off the trivial branch, complete with all secondary bifurcations, for parameter values between 0 and 80. The dimension of the unstable manifold for the flow is determined at some stationary solution in each branch.
[Vladimir Mityushev (Kraków)]

MSC 2000:: *35B32 Bifurcation (PDE)
35K55 Nonlinear parabolic equations
37M20 Computational methods for bifurcation problems
70K50 Transition to stochasticity (general mechanics)

Keywords: Kuramoto-Sivashinski equation; bifurcation diagram

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]