Integral manifolds for partial functional differential equations in admissible spaces on a half-line
http://repository.vnu.edu.vn/handle/VNU_123/32187
In this paper we investigate the existence of stable and center-stable manifolds for solutions to partial functional differential equations of the form u̇(t)=A(t)u(t)+f(t,ut), t≥0, when its linear part, the family of operators (A(t))t≥0, generates the evolution family (U(t, s))t≥s≥0 having an exponential dichotomy or trichotomy on the half-line and the nonlinear forcing term f satisfies the φ-Lipschitz condition, i.e., {norm of matrix}f(t,ut)-f(t,vt){norm of matrix}≤φ(t){norm of matrix}ut-vt{norm of matrix}C where ut,vt∈C:=C([-r,0],X), and φ(t) belongs to some admissible function space on the half-line.
Our main methods invoke Lyapunov-Perron methods and the use of admissible function spaces
In this paper we investigate the existence of stable and center-stable manifolds for solutions to partial functional differential equations of the form u̇(t)=A(t)u(t)+f(t,ut), t≥0, when its linear part, the family of operators (A(t))t≥0, generates the evolution family (U(t, s))t≥s≥0 having an exponential dichotomy or trichotomy on the half-line and the nonlinear forcing term f satisfies the φ-Lipschitz condition, i.e., {norm of matrix}f(t,ut)-f(t,vt){norm of matrix}≤φ(t){norm of matrix}ut-vt{norm of matrix}C where ut,vt∈C:=C([-r,0],X), and φ(t) belongs to some admissible function space on the half-line.
Our main methods invoke Lyapunov-Perron methods and the use of admissible function spaces
| Title: | Integral manifolds for partial functional differential equations in admissible spaces on a half-line |
| Authors: | Huy, Thieu Nguyen Viet Duoc, Trinh |
| Keywords: | Admissibility of function spaces Exponential dichotomy and trichotomy Partial functional differential equations Stable and center-stable manifolds |
| Issue Date: | 2014 |
| Publisher: | Journal of Mathematical Analysis and Applications |
| Citation: | Scopus |
| Abstract: | In this paper we investigate the existence of stable and center-stable manifolds for solutions to partial functional differential equations of the form u̇(t)=A(t)u(t)+f(t,ut), t≥0, when its linear part, the family of operators (A(t))t≥0, generates the evolution family (U(t, s))t≥s≥0 having an exponential dichotomy or trichotomy on the half-line and the nonlinear forcing term f satisfies the φ-Lipschitz condition, i.e., {norm of matrix}f(t,ut)-f(t,vt){norm of matrix}≤φ(t){norm of matrix}ut-vt{norm of matrix}C where ut,vt∈C:=C([-r,0],X), and φ(t) belongs to some admissible function space on the half-line. Our main methods invoke Lyapunov-Perron methods and the use of admissible function spaces |
| Description: | Journal of Mathematical Analysis and Applications,Volume 411, Issue 2, 15 March 2014, Pages 816-828 Journal of Mathematical Analysis and Applications |
| URI: | http://www.sciencedirect.com/science/article/pii/S0022247X13009311 http://repository.vnu.edu.vn/handle/VNU_123/32187 |
| ISSN: | 0022247X |
| Appears in Collections: | Bài báo của ĐHQGHN trong Scopus |
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