Center manifolds and dynamics near equilibria of quasilinear parabolic systems with fully nonlinear boundary conditions | Zendy

Ronald Schnaubelt | Zendy; Jan Prüß | Zendy; Yuri Latushkin | Zendy

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Center manifolds and dynamics near equilibria of quasilinear parabolic systems with fully nonlinear boundary conditions

Author(s) -

Ronald Schnaubelt,

Jan Prüß,

Yuri Latushkin

Publication year - 2008

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2008.9.595

Subject(s) - center manifold , center (category theory) , nonlinear system , bounded function , manifold (fluid mechanics) , mathematical analysis , mathematics , partial differential equation , boundary (topology) , invariant manifold , boundary value problem , physics , bifurcation , mechanical engineering , chemistry , hopf bifurcation , quantum mechanics , engineering , crystallography

We study quasilinear systems of parabolic partial differential equa- tions with fully nonlinear boundary conditions on bounded or exterior domains. Our main results concern the asymptotic behavior of the solutions in the vicin- ity of an equilibrium. The local center, center-stable, and center-unstable manifolds are constructed and their dynamical properties are established using nonautonomous cutoff functions. Under natural conditions, we show that each solution starting close to the center manifold converges to a solution on the center manifold.

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