کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4615076 1339307 2015 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Well-posedness for nonlinear Schrödinger equations with boundary forces in low dimensions by Strichartz estimates
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Well-posedness for nonlinear Schrödinger equations with boundary forces in low dimensions by Strichartz estimates
چکیده انگلیسی

In this paper, we study the well-posedness of solutions for nonlinear Schrödinger equations on one and two dimensional domains with boundary where the boundary is disturbed by an external inhomogeneous type of Dirichlet or Neumann force. We first prove the local existence of solutions at the energy level for quadratic and superquadratic sources using the Strichartz estimates on domains. Secondly, we obtain conditional uniqueness and local stability. Then, we prove the boundedness of solutions in the energy space to pass from the local theory to the global theory. Regarding subquadratic sources, we appeal to classical methods and Trudinger's inequality to prove the uniqueness, which, combined with the existence of weak energy solutions, mass and energy inequalities, eventually implies the continuity of solutions in time.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 424, Issue 1, 1 April 2015, Pages 487–508
نویسندگان
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