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The aim of this paper is to prove the existence of an admissible inertial manifold for mild solutions to infinite delay evolution equation of the form $$ \left \{ \begin{aligned} \frac{du}{dt}+Au & =F(t,u_t), \quad t\geq s, \medskip \\ u_s (\theta)&=\phi(\theta), \ \ \forall \theta \in ( -\infty, 0], \ \ s \in \R, \quad \end{aligned} \right. $$ where $A$ is positive definite and self-adjoint with a discrete spectrum, the Lipschitz coefficient of the nonlinear part $F$ may depend on time and belongs to some admissible function space defined on the whole line. The proof is based on the Lyapunov-Perron equation in combination with admissibility and duality estimates.
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참고문헌 (7)
참고문헌 신청
L. Boutet de Monvel / 1998 / Inertial manifolds for retarded semilinear parabolic equations / Nonlinear Analysis: Theory, Methods & Applications 34(6):907~925
I. D. Chueshov / 2002 / Introduction to the Theory of Infinite-Dimensional Dissipative Systems / ACTA Scientific Publishing House
P. Constantin / 1989 / Integral manifolds and inertial manifolds for dissipative partial differential equations / Springer-Verlag
Ciprian Foias / 1988 / Inertial manifolds for nonlinear evolutionary equations / Journal of Differential Equations 73(2):309~353
Thieu Huy Nguyen / 2013 / Admissibly inertial manifolds for a class of semi-linear evolution equations / Journal of Differential Equations 254(6):2638~2660
I. D. Chueshov / 2002 / Introduction to the Theory of Infinite-Dimensional Dissipative Systems / ACTA Scientific Publishing House
P. Constantin / 1989 / Integral manifolds and inertial manifolds for dissipative partial differential equations / Springer-Verlag
Ciprian Foias / 1988 / Inertial manifolds for nonlinear evolutionary equations / Journal of Differential Equations 73(2):309~353
Thieu Huy Nguyen / 2013 / Admissibly inertial manifolds for a class of semi-linear evolution equations / Journal of Differential Equations 254(6):2638~2660
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