Asymptotics of solutions to a nonlinear parabolic equation in the neighborhood of front formation (Q1395187)

This paper is devoted to a Cauchy problem for the implicitly degenerate equation \(u_t={u^\alpha}u_{xx}\), \(0<{\alpha}<1\). The initial function vanishes on a half-line. The short-time behavior of a solution is analyzed in the neighborhood of the origin. An asymptotic solution and asymptotics of the front boundary are constructed for \(t\longrightarrow{0}\).