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Báo cáo hóa học: " Research Article Cauchy-Neumann Problem for Second-Order ¨ General Schrodinger Equations in Cylinders with Nonsmooth Bas"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Cauchy-Neumann Problem for Second-Order ¨ General Schrodinger Equations in Cylinders with Nonsmooth Bas | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 231802 13 pages doi 10.1155 2009 231802 Research Article Cauchy-Neumann Problem for Second-Order General Schrodinger Equations in Cylinders with Nonsmooth Bases Nguyen Manh Hung 1 Tran Xuan Tiep 2 and Nguyen Thi Kim Son1 1 Department of Mathematics Hanoi University of Education Hanoi Vietnam 2 Faculty of Applied Mathematics and Informatics Hanoi University of Technology Hanoi Vietnam Correspondence should be addressed to Nguyen Thi Kim Son mt02_02@yahoo.com Received 26 February 2009 Accepted 18 June 2009 Recommended by Gary Lieberman The main goal of this paper is to obtain the regularity of weak solutions of Cauchy-Neumann problems for the second-order general Schrodinger equations in domains with conical points on the boundary of the bases. Copyright 2009 Nguyen Manh Hung et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction and Notations Cauchy-Dirichlet problem for general Schrodinger systems in domains containing conical points has been investigated in 1 2 . Cauchy-Neumann problems have been dealt with for hyperbolic systems in 3 and for parabolic equations in 4-6 . In this paper we consider the Cauchy-Neumann problem for the second-order general Schrodinger equations in infinite cylinders with nonsmooth bases. The solvability of this problem has been considered in 7 . Our main purpose here is to study the regularity of weak solution of the mentioned problem. The paper consists of six sections. In Section 1 we introduce some notations and functional spaces used throughout the text. A weak solution of the problem is defined in Section 2 together with some results of its unique existence and smoothness with the time variable. Our main result the regularity with respect to both of time and spatial variables of