tailieunhanh - báo cáo hóa học:" Research Article A Mixed Problem for Quasilinear Impulsive Hyperbolic Equations with Non Stationary Boundary and Transmission Conditions"

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 A Mixed Problem for Quasilinear Impulsive Hyperbolic Equations with Non Stationary Boundary and Transmission Conditions | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 101959 19 pages doi 2010 101959 Research Article A Mixed Problem for Quasilinear Impulsive Hyperbolic Equations with Non Stationary Boundary and Transmission Conditions Akbar B. Aliev1 and Ulviya M. Mamedova2 1 Azerbaijan Technical University AZ 1073 Baki Azerbaijan 2 Institute of Mathematics and Mechanics of NAS of Azerbaijan AZ 1141 Baku Azerbaijan Correspondence should be addressed to Akbar B. Aliev aliyevagil@ Received 10 March 2010 Revised 13 June 2010 Accepted 26 October 2010 Academic Editor Toka Diagana Copyright 2010 A. B. Aliev and U. M. Mamedova. 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. The initial-boundary value problem for a class of linear and nonlinear equations in Hilbert space is considers. We prove the existence and uniqueness of solution of this problem. The results of this investigation are applied to solvability of initial-boundary value problems for quasilinear impulsive hyperbolic equations with non-stationary transmission and boundary conditions. 1. Abstract Model Initial Boundary Value Problem with Non Stationary Boundary and Transmission Conditions for the Impulsive Linear Hyperbolic Equations In paper 1 there is given an abstract scheme of investigation of mixed problems for hyperbolic equations with non stationary boundary conditions. In this direction some results were obtained in 2 . In this paper we offer the analogues abstract model of investigation of mixed problem with non stationary boundary and transmission conditions for impulsive linear and semilinear hyperbolic equations. . Statement of the Problem and Main Theorem Let Hi Hl0 XV Y1 v 1 2 . Si i 1 2 . m p. 1 2 . Tj j 1 2 . m be Hilbert Spaces. Consider the following abstract initial-boundary value problem 2