关键词: Burgers equation, Hopf equation, nonhomogeneous equation

Abstract:

In [1], Ding et al. studied the nonhomogeneous Burgers equation
$$ u_t+uu_x=\mu u_{xx}+4x.\eqno{(1.1)}$$

This paper  will
 prove that when $\mu\to 0$ the solution of (1.1) will approach the
generalized solution of
$$ u_t+uu_x=4x.\eqno{(1.2)}$$
The authors notice that the equation (1.2) is beyond the scope of
investigations by Oleinik O. in [2]. The solutions here are
unbounded in general.

The paper also studies the $\d$-wave phenomenon when (1.2) is jointed with
some other equation.

Key words: Burgers equation, Hopf equation, nonhomogeneous equation