Logarithmic asymptotics of rapidly decreasing solutions of Petrovskij hyperbolic equations
type: Item
instance of: scholarly article
title: Logarithmic asymptotics of rapidly decreasing solutions of Petrovskij hyperbolic equations
zbMATH Open document ID: 0698.35014
DOI: 10.1007/BF01157932
author: V. P. Maslov
author: M. V. Fedoryuk
published in: Mathematical Notes
publication date: 1989-01-01T00:00:00Z
review text: The Cauchy problem for the homogeneous, in Petrovskij's sense hyperbolic equation \((1)\quad L(\partial /\partial t,\partial /\partial x)u=0,\) \(t>0\), \(x\in R^ n\) is considered. The existence of the limit \(\lim_{\lambda \to \infty}(\ell n(u(t,x))/\lambda)=S(t,x)\) is proved. Here \(\lambda\) is a parameter arising in the initial conditions. Also, it is shown that the function S is continuous and in the points of smoothness it satisfies the Hamilton-Jacobi equation \(L(\partial S/\partial t,\partial S/\partial x)u=0\) which is associated to (1).
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 35L30
zbMATH DE Number: 4144462
zbMATH Keywords: Petrovskij hyperbolicity
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Hamilton-Jacobi equation
reviewed by: Violeta A. Kostova
MaRDI profile type: Publication
cites work: Q3951314
cites work: Q3280274
cites work: Lacunas for hyperbolic differential operators with constant coefficients.I
cites work: Q3334648
description: scientific article; zbMATH DE number 4144462