Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing – a computer assisted proof. (English) Zbl 1312.65170

Cyranka, Jacek; Zgliczyński, Piotr

SIAM J. Appl. Dyn. Syst. 14, No. 2, 787-821 (2015).

Summary: We prove the existence of globally attracting solutions of the viscous Burgers equation with periodic boundary conditions on the interval for some particular choices of viscosity and nonautonomous forcing. The attracting solution is periodic if the forcing is periodic. The method is general and can be applied to other similar partial differential equations. The proof is computer assisted.

MSC:

65M99	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35B40	Asymptotic behavior of solutions to PDEs
35Q53	KdV equations (Korteweg-de Vries equations)
37B55	Topological dynamics of nonautonomous systems
65G40	General methods in interval analysis

Keywords:

viscous Burgers equation; periodic boundary conditions; nonautonomous forcing; attractor; rigorous numerics; interval arithmetic; logarithmic norm; computer assisted proof; self-consistent bounds

Software:

CAPD

References:

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