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: On the regularity of the solution for the second initial boundary value problem for hyperbolic systems in domains with conical points | Hung et al. Boundary Value Problems 2011 2011 17 http content 2011 1 17 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access On the regularity of the solution for the second initial boundary value problem for hyperbolic systems in domains with conical points Nguyen Manh Hung 1 Nguyen Thanh Anh1 and Phung Kim Chuc2 Correspondence thanhanh@ department of Mathematics Hanoi National University of Education Hanoi Vietnam Full list of author information is available at the end of the article Springer Abstract In this paper we deal with the second initial boundary value problem for higher order hyperbolic systems in domains with conical points. We establish several results on the well-posedness and the regularity of solutions. 1 Introduction Boundary value problems in nonsmooth domains have been studied in differential aspects. Up to now elliptic boundary value problems in domains with point singularities have been thoroughly investigated see 1 2 and the extensive bibliography in this book . We are concerned with initial boundary value problems for hyperbolic equations and systems in domains with conical points. These problems with the Dirichlet boundary conditions were investigated in 3-5 in which the unique existence the regularity and the asymptotic behaviour near the conical points of the solutions are established. The Neumann boundary problem for general second-order hyperbolic systems with the coefficients independent of time in domains with conical points was studied in 6 . In the present paper we consider the Cauchy-Neumann the second initial boundary value problem for higher-order strongly hyperbolic systems in domains with conical points. Our paper is organized as follows. Section 2 is devoted to some notations and the formulation of the problem. In Section 3 we present the results on the unique existence and the regularity in time of the generalized solution. The global regularity of the solution is
