tailieunhanh - Báo cáo hóa học: " Neumann problem on the semi-line for the Burgers equation"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài : Neumann problem on the semi-line for the Burgers equation | De Lillo and Sommacal Boundary Value Problems 2011 2011 34 http content 2011 1 34 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access Neumann problem on the semi-line for the Burgers equation Silvana De Lillo1 2 and Matteo Sommacal3 Correspondence sommacal@ihes. fr 3Institut des Hautes Etudes Scientifiques 91440 Bures-sur- Yvette France Full list of author information is available at the end of the article Abstract In this article the Neumann problem on the semi-line for the Burgers equation is considered. The problem is reduced to a nonlinear integral equation in one independent variable whose unique solution is proven to exist for small time. An explicit solution is discussed as well. Keywords Burgers equation Neumann problem 1 Introduction Initial boundary value IBV problems for integrable nonlinear PDEs frequently appear in physical applications and have originated several important studies in the past few decades. Much interest has been devoted to IBV problems for nonlinear PDEs which are treatable by the inverse scattering transform method such as the nonlinear Shro-dinger equation NLS the Korteweg-de Vries equation KdV and the Sine-Gordon equation 1-8 . Other studies have been devoted to IBV problems for nonlinear PDEs which are C-integrable namely which are exactly linearizable via a change of variables well-known examples in this class are the Burgers equation and the Eckhaus equation 9-15 . It is the aim of this article to analyze the Neumann problem for the Burgers equation Ut Uxx 2UxU u u x t 1 on the semi-infinite domain x e 0 characterized by the following set of initial and boundary data u x 0 U0 x x 0 2a Ux 0 t F t t 0 2b with F 0 U0x 0 2c where F t is a continuous bounded function of its argument F t B B e R 2d Springer 2011 De Lillo and Sommacal licensee Springer. This is an Open Access article distributed underthe terms ofthe Creative Commons Attribution License http licenses by