Viscosity method of a non-homogeneous Burgers equation

In [1], Ding et al. studied the nonhomogeneous Burgers equation u(t) + uu(x) = muu(xx) + 4x. (1.1) This paper will prove that when mu --> 0 the solution of (1.1) will approach the generalized solution of u(t) + uu(x) = 4x. (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 delta-wave phenomenon when (1.2) is jointed with some other equation.