A remark on removable singularity for nonlinear convection–diffusion equation

In this paper we study the following Cauchy problem: ut=uxx+(un)x,(x,t)∈R×(0,∞),u(x,0)=δ(x),x∈R, where δ(x)δ(x) is a Dirac measure and n≥0n≥0. Its solution is called source-type solution. Such singular solution plays an important role in the development of theory of nonlinear parabolic equations. However, there seems not to be perfect answer to the research. Here we focus on whether there is a critical exponent n0n0 such that when n