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Asymptotics for the Burgers Equation with Pumping

Authors:	Nakao Hayashi Pavel I Naumkin

Institution:	(1) Department of Mathematics, Graduate School of Science, Osaka University, Osaka, Toyonaka, 560-0043, Japan;(2) Instituto de Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia, CP 58089 Michoacán, Mexico

Abstract:	We consider the large time asymptotic behavior of solutions to the initial-boundary value problem $\left\{u_{t}+e^{t}u u_{x}-u_{xx}=0,x\in {\bf R,}t>0, u\left( 0,x\right) =u_{0}\left( x\right),x\in {\bf R,} u\left( t,x\right) \rightarrow a_{\pm }, x\rightarrow \pm \infty , t>0.\right.$ We find large time asymptotic formulas of solutions for three different cases 1) a_±=±1, 2) a_±=1 and 3) a_±=0.

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