کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772310 | 1413359 | 2017 | 48 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The point-like limit for a NLS equation with concentrated nonlinearity in dimension three
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We consider a scaling limit of a nonlinear Schrödinger equation (NLS) with a nonlocal nonlinearity showing that it reproduces in the limit of cutoff removal a NLS equation with nonlinearity concentrated at a point. The regularized dynamics is described by the equationiââtÏε(t)=âÎÏε(t)+g(ε,μ,|(Ïε,Ïε(t))|2μ)(Ïε,Ïε(t))Ïε where Ïεâδ0 weakly and the function g embodies the nonlinearity and the scaling and has to be fine tuned in order to have a nontrivial limit dynamics. The limit dynamics is a nonlinear version of point interaction in dimension three and it has been previously studied in several papers as regards the well-posedness, blow-up and asymptotic properties of solutions. Our result is the first justification of the model as the point limit of a regularized dynamics.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 273, Issue 5, 1 September 2017, Pages 1762-1809
Journal: Journal of Functional Analysis - Volume 273, Issue 5, 1 September 2017, Pages 1762-1809
نویسندگان
Claudio Cacciapuoti, Domenico Finco, Diego Noja, Alessandro Teta,