کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4611758 1338638 2009 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Regularity of invariant sets in semilinear damped wave equations
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Regularity of invariant sets in semilinear damped wave equations
چکیده انگلیسی

Under fairly general assumptions, we prove that every compact invariant subset II of the semiflow generated by the semilinear damped wave equationϵutt+ut+β(x)u−∑ij(aij(x)uxj)xi=f(x,u),(t,x)∈[0,+∞[×Ω,u=0,(t,x)∈[0,+∞[×∂Ω, in H01(Ω)×L2(Ω) is in fact bounded in D(A)×H01(Ω). Here Ω   is an arbitrary, possibly unbounded, domain in R3R3, Au=β(x)u−∑ij(aij(x)uxj)xiAu=β(x)u−∑ij(aij(x)uxj)xi is a positive selfadjoint elliptic operator and f(x,u)f(x,u) is a nonlinearity of critical growth. The nonlinearity f(x,u)f(x,u) needs not to satisfy any dissipativeness assumption and the invariant subset II needs not to be an attractor.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 247, Issue 12, 15 December 2009, Pages 3315–3337
نویسندگان
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