Mixed problems or Cauchy problems for semi-degenerate hyperbolic equations of 2-nd order with a parameter
type: Item
instance of: scholarly article
title: Mixed problems or Cauchy problems for semi-degenerate hyperbolic equations of 2-nd order with a parameter
zbMATH Open document ID: 0777.35039
author: Reiko Sakamoto
published in: Journal of Mathematics of Kyoto University
publication date: 1993-04-19T00:00:00Z
review text: The author considers mixed problems or Cauchy problems for semi- degenerate hyperbolic equations of second order. She constructs two typical examples of operators: \[ (1)\quad L=\partial^ 2_ t- \rho\partial^ 2_ 1-\partial^ 2_ 2-(\mu+1)\partial_ 1,\qquad(2)\quad L=\partial^ 2_ t-\partial^ 2_ 1-\partial^ 2_ 2-(\mu+1)\rho^{-1}\partial_ 1, \] where \(\mu\) is a parameter, \(\rho\) is a \(C^ \infty\)-function and equals \(x_ 1\) near \(x_ 1=0\). These two examples represent the degenerate case and the singular case, respectively. Then the author discusses existence and uniqueness of solutions of mixed problems or Cauchy problems for these two operators with the paramter ranging in different intervals.
Mathematics Subject Classification ID: 35L35
Mathematics Subject Classification ID: 35L30
Mathematics Subject Classification ID: 35L80
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 109385
zbMATH Keywords: mixed problems
zbMATH Keywords: Cauchy problems
zbMATH Keywords: semi-degenerate hyperbolic equations of second order
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
reviewed by: Shuxing Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519538
OpenAlex ID: W1565164799
DOI: 10.1215/KJM/1250519538
description: scientific article; zbMATH DE number 109385