Stability, instability and center manifold theorem for fully nonlinear autonomous parabolic equations in Banach space. (English) Zbl 0661.35044

Da Prato, G.; Lunardi, A.

Arch. Ration. Mech. Anal. 101, No. 2, 115-141 (1988).

The authors study fully nonlinear equations of parabolic type. They deal with stability, instability and saddle points of an equilibrium and establish the existence of an attracting local center manifold.

Reviewer: J.F.Bonnans

MSC:

35K55	Nonlinear parabolic equations
35B40	Asymptotic behavior of solutions to PDEs
37-XX	Dynamical systems and ergodic theory
35K15	Initial value problems for second-order parabolic equations

Keywords:

fully nonlinear; stability; instability; saddle points; equilibrium; existence; attracting local center manifold