The uniqueness and existence of solution of this seccond innitial boundary problem for second-order Schrödinger equation in cylinders with nonsmooth bases

Phung Kim Chuc *

* Corresponding author (pkchuc@ctu.edu.vn)

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Received: 20 Apr 2021
Accepted: 22 Dec 2016
Published: 23 Dec 2016
Title: The uniqueness and existence of solution of this seccond innitial boundary problem for second-order Schrödinger equation in cylinders with nonsmooth bases
DOI: 10.22144/ctu.jvn.2016.608
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How to Cite
Chức, P. K. (2016). The uniqueness and existence of solution of this seccond innitial boundary problem for second-order Schrödinger equation in cylinders with nonsmooth bases. CTU Journal of Science, (47), 114-119. https://doi.org/10.22144/ctu.jvn.2016.608
Issue
No. 47 (2016)
Section
Natural Sciences

Abstract

Cauchy-Dirichlet problem for the general Schrödinger systems in domains containing conical points has been investigated by Nguyen Manh Hung (1998).  In this paper, we study the second initial boundary value problem for second-order Schrödinger equations   in cylinders with nonsmooth bases . The purpose of this paper is to study the unique solvability of generalized solution of the problem.
Keywords: Second initial boundary value problem, Schrödinger equation, generalized solution, cylinders with nonsmooth bases

Tóm tắt

Bài toán Cauchy-Dirichlet đối với hệ phương trình Schrödinger tổng quát trong miền chứa điểm nón đã được tác giả Nguyen Manh Hung (1998) nghiên cứu. Trong bài báo này, chúng tôi  nghiên cứu về bài toán biên ban đầu thứ hai đối với phương trình   Schrödinger cấp hai trong hình trụ đáy không trơn . Bài báo trình bày kết quả về sự tồn tại duy nhất của nghiệm suy rộng.
Từ khóa: Bài toán biên ban đầu thứ hai, phương trình Schödinger, nghiệm suy rộng, hình trụ đáy không trơn

Article Details

References

R. A. Adams (1975), Sobolev spaces, Academic Press.

Nguyen Manh Hung and Phung Kim Chuc (2014), "Asymptotic of solutions for second IBVP for hyperbolic systems in non-smooth domains". Vol. 93, No. 5, pp. 1010-1035. Applicable Analysis 2014.

Nguyen Manh Hung and Phung Kim Chuc (2012), "On the smoothness of the solution for the initial - Neumann problem for hyperbolic systems in Lipschitz cylinders". Vol. 16, No. 5,pp. 1629-1645,October 2012; Taiwanese Journal of Mathematics.

Nguyen Manh Hung and Nguyen Thi Kim Son (2008), " Existence and smoothness of solutions to the second initial boundary value problem for Schrödinger systems in cylinders with non-smooth base".Vol 2008. No. 35. pp.1- 11. Electronic Journal of Differential Equations.

Nguyen Manh Hung, (1998), "The first initial boundary value problem for Schrödinger systems in non-smooth domains", Diff Urav., 34 (1998), pp 1546-1556 (in Russian).

Lions, J. L. And Magenes, E; (1972) “Non-homogeneous boundary value problems and applications” Vol 1,2 Springer, 1972.