کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4615999 1339334 2014 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An attractor for the singularly perturbed Kirchhoff equation with supercritical nonlinearity
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
An attractor for the singularly perturbed Kirchhoff equation with supercritical nonlinearity
چکیده انگلیسی


• We prove the existence of a global attractor on an appropriate phase space.
• We do not make any growth restrictions on the nonlinearity f(u)f(u).
• The smallness assumption for the initial data can be replaced by the smallness of ϵ.

We consider a quasilinear wave equation of Kirchhoff typeϵutt−(1+‖∇u‖2)Δu+ut+f(u)=g(x),ϵutt−(1+‖∇u‖2)Δu+ut+f(u)=g(x), where ϵ>0ϵ>0 is a small parameter. Without any growth restrictions on the nonlinearity f(u)f(u), we prove the existence of a finite-dimensional global attractor on an appropriate (bounded) phase space. The key step is the estimate of the difference between the solutions of a quasilinear dissipative hyperbolic equation of Kirchhoff type and the corresponding quasilinear parabolic equation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 411, Issue 1, 1 March 2014, Pages 240–253
نویسندگان
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