Admissibly integral manifolds for semilinear evolution equations

• Autorzy: Nguyen Thieu Huy , Vu Thi Ngoc Ha
• Języki publikacji: EN

Abstrakty

EN

We prove the existence of integral (stable, unstable, center) manifolds of admissible classes for the solutions to the semilinear integral equation $u(t) = U(t,s)u(s) + ∫_s^t U(t,ξ)f(ξ,u(ξ))dξ$ when the evolution family $(U(t,s))_{t≥s}$ has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term f satisfies the (local or global) φ-Lipschitz conditions, i.e., ||f(t,x)-f(t,y)|| ≤ φ(t)||x-y|| where φ(t) belongs to some classes of admissible function spaces. These manifolds are formed by trajectories of the solutions belonging to admissible function spaces which contain wide classes of function spaces like function spaces of $L_p$ type, the Lorentz spaces $L_{p,q}$ and many other function spaces occurring in interpolation theory. Our main methods involve the Lyapunov-Perron method, rescaling procedures, and techniques using the admissibility of function spaces.

Kategorie tematyczne

• 34C45: Invariant manifolds
• 34D09: Dichotomy, trichotomy
• 35B40: Asymptotic behavior of solutions
• 34G20: Nonlinear equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2014
• Tom: 112
• Numer: 2
• Strony: 127-163

Daty

wydano

2014

Twórcy

autor

Nguyen Thieu Huy

• Arbeitsgruppe Angewandte Analysis, Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
• School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Vien Toan ung dung va Tin hoc, Dai hoc Bach khoa Hanoi, 1 Dai Co Viet, Hanoi, Vietnam

autor

Vu Thi Ngoc Ha

• School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Vien Toan ung dung va Tin hoc, Dai hoc Bach khoa Hanoi, 1 Dai Co Viet, Hanoi, Vietnam

Identyfikatory

DOI

10.4064/ap112-2-3