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: Spatial estimates for a class of hyperbolic equations with nonlinear dissipative boundary conditions | Tahamtani and Peyravi Boundary Value Problems 2011 201 1 19 0 Boundary Value Problems http content 2011 1 19 a SpringerOpen Journal RESEARCH Open Access Spatial estimates for a class of hyperbolic equations with nonlinear dissipative boundary conditions Faramarz Tahamtani and Amir Peyravi Correspondence tahamtani@ Department of Mathematics College of Sciences Shiraz University Shiraz 71454 Iran Abstract This paper is concerned with investigating the spatial behavior of solutions for a class of hyperbolic equations in semi-infinite cylindrical domains where nonlinear dissipative boundary conditions imposed on the lateral surface of the cylinder. The main tool used is the weighted energy method. Mathematics Subject Classification 2010 35B40 35L05 35L35 Keywords Hyperbolic equation Nonlinear boundary conditions Phragmen-Lindelof type theorem Asymptotic behavior 1 Introduction The aim of this paper is to study the spatial asymptotic behavior of solutions of the problem determined by the equation utt Aut aut A2u x t e 1 X 0 to 1 1 where a is a positive constant and Q x e Rn Xn e R x xi . Xn 1 e Txn c Rn 1 where hr x xn e xn T . When we consider equation we impose the initial and boundary conditions u x 0 ut x 0 0 x e . du u X 0 t h1 x t dv x 0 t h2 X t x t e r0 X 0 to Jd u u 0 Au fl d 1 x t e s0 X 0 to where V is the outward normal to the boundary and Sr x e Rn x e 3Fxn T xn to Springer 2011 Tahamtani and Peyravi licensee Springer. This is an Open Access article distributed under the terms ofthe Creative Commons Attribution License http licenses by which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Tahamtani and Peyravi Boundary Value Problems 2011 2011 19 http content 2011 1 19 Page 2 of 9 where T rT is a map from R into family of bounded domains in Rn-1 with sufficiently smooth boundary .
