Tupchiev, V. A. Asymptotic of a solution to the initial-boundary value problem for a generalized Burger’s equation. (Russian, English) Zbl 1121.35338 Zh. Vychisl. Mat. Mat. Fiz. 44, No. 1, 152-165 (2004); translation in Comput. Math. Math. Phys. 44, No. 1, 141-154 (2004). The boundary problem in a rectangular domain \(\Pi ^T ={(x,t): 0<x<l, 0<t<T}\) for the equation \[ u_t + f (u)_x = \mu u_{xx}, \quad \tag{1} \] where the initial conditions have the form \[ u(x, 0)= u^0(x) \quad \tag{2} \] and the boundary conditions are \[ u(0,t) = 0, \quad u(l,t)= \psi (t) , \quad \tag{3} \] with some additional conditions for the functions \(f(u), u^0(x), \psi (t)\) is discussed. When \(f(u)=u^2/2\) the equation (1) is called Burger’s equation. Here the initial-boundary problem (1)–(3) for a generalized Burger’s equation (1) is considered. An asymptotic expansion of a high order in relation to a small viscous parameter is constructed and justified. Reviewer: Sergei Zhuravlev (Moskva) MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35C20 Asymptotic expansions of solutions to PDEs Keywords:boundary value problems for non-linear high-order PDE; generalized Burger,s equation; compressible viscous fluid motion PDFBibTeX XMLCite \textit{V. A. Tupchiev}, Zh. Vychisl. Mat. Mat. Fiz. 44, No. 1, 152--165 (2004; Zbl 1121.35338); translation in Comput. Math. Math. Phys. 44, No. 1, 141--154 (2004)