Two-parameter asymptotics in the Cauchy problem for a quasi-linear parabolic equation

Abstract

The Cauchy problem for a quasi-linear parabolic equation with a small parameter ε at the higher derivative is considered. The derivative of the initial function is of order O(1/ρ), where ρ is another small parameter. We study the asymptotics of the solution of the problem in parameters ε and ρ tending to zero.