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Title: Well-posedness for nonlinear Schrödinger equations with boundary forces in low dimensions by Strichartz estimates
Authors: Özsarı, Türker
Keywords: Conditional uniqueness
Inhomogeneous boundary conditions
Local and global existence
Nonlinear Schrödinger equation
Strichartz estimates
Issue Date: Apr-2015
Publisher: Academic Press Inc.
Source: Özsarı, T. (2015). Well-posedness for nonlinear Schrödinger equations with boundary forces in low dimensions by Strichartz estimates. Journal of Mathematical Analysis and Applications, 424(1), 487-508. doi:10.1016/j.jmaa.2014.11.034
Abstract: 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.
ISSN: 0022-247X
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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