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Asymptotics for the Burgers Equation with Pumping
Authors:Nakao Hayashi  Pavel I. Naumkin
Affiliation:(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 $$left{u_{t}+e^{t}u u_{x}-u_{xx}=0,xin {bf R,}t>0,  uleft( 0,xright) =u_{0}left( xright),xin {bf R,}  uleft( t,xright) rightarrow a_{pm }, xrightarrow pm infty , t>0.right.$$ We find large time asymptotic formulas of solutions for three different cases 1) a±=±1, 2) a±=mnplus1 and 3) a±=0.
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