کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
840786 908492 2012 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Exponential attractors for semigroups in Banach spaces
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Exponential attractors for semigroups in Banach spaces
چکیده انگلیسی

Let {S(t)}t⩾0{S(t)}t⩾0 be a semigroup on a Banach space XX, and AA be the global attractor for {S(t)}t⩾0{S(t)}t⩾0.We assume that there exists a T∗T∗ such that S≜S(T∗)S≜S(T∗) is of class C1C1 on a bounded absorbing set Bϵ0(A)Bϵ0(A) and S:Bϵ0(A)→Bϵ0(A)S:Bϵ0(A)→Bϵ0(A), and furthermore, the linearized operator LL at each point of Bϵ0(A)Bϵ0(A) can be decomposed as L=K+CL=K+C with KK compact and ‖C‖<λ<1‖C‖<λ<1; then we prove the existence of an exponential attractor for the discrete semigroup {Sn}n=1∞ in the Banach space XX. And then we apply the standard approach of Eden et al. (1994) [9] to obtain the continuous case. Here Bϵ0(A)Bϵ0(A) denotes the ϵ0ϵ0-neighborhood of AA in Banach space XX, and ‖C‖‖C‖ denotes the norm of the operator CC.We prove, as a simple application, the existence of an exponential attractor for some nonlinear reaction–diffusion equations with polynomial growth nonlinearity of arbitrary order.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 75, Issue 4, March 2012, Pages 1799–1809
نویسندگان
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