کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4621740 | 1339488 | 2008 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Regularity of solutions on the global attractor for a semilinear damped wave equation
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
We consider attractors Aη, ηâ[0,1], corresponding to a singularly perturbed damped wave equationutt+2ηA12ut+aut+Au=f(u) in H01(Ω)ÃL2(Ω), where Ω is a bounded smooth domain in R3. For dissipative nonlinearity fâC2(R,R) satisfying |fâ³(s)|⩽c(1+|s|) with some c>0, we prove that the family of attractors {Aη,η⩾0} is upper semicontinuous at η=0 in H1+s(Ω)ÃHs(Ω) for any sâ(0,1). For dissipative fâC3(R,R) satisfying lim|s|ââfâ³(s)s=0 we prove that the attractor A0 for the damped wave equationutt+aut+Au=f(u) (case η=0) is bounded in H4(Ω)ÃH3(Ω) and thus is compact in the Hölder spaces C2+μ(Ω¯)ÃC1+μ(Ω¯) for every μâ(0,12). As a consequence of the uniform bounds we obtain that the family of attractors {Aη,ηâ[0,1]} is upper and lower semicontinuous in C2+μ(Ω¯)ÃC1+μ(Ω¯) for every μâ(0,12).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 337, Issue 2, 15 January 2008, Pages 932-948
Journal: Journal of Mathematical Analysis and Applications - Volume 337, Issue 2, 15 January 2008, Pages 932-948
نویسندگان
A.N. Carvalho, J.W. Cholewa,