Asymptotic Solution of the Multidimensional Burgers Equation Near A Singularity

Abstract

We consider the Cauchy problem for the multidimensional Burgers equation with a small dissipation parameter and use the matching method to construct an asymptotic solution near the singularity determined by the vector field structure at the initial instant. The method that we use allows tracing the evolution of the solution with a hierarchy of differently scaled structures and giving a rigorous mathematical definition of the asymptotic solution in the leading approximation. We discuss the relation of the considered problem to different models in fundamental and applied physics.