Boundary value problems for non-Cauchy-Kovalevskaya-type systems in a quarter-space
type: Item
instance of: scholarly article
title: Boundary value problems for non-Cauchy-Kovalevskaya-type systems in a quarter-space
zbMATH Open document ID: 0864.35084
published in: Siberian Advances in Mathematics
publication date: 1996-08-20T00:00:00Z
review text: An initial-boundary value problem in a quarter space for a sufficiently large class of integro-differential systems with degenerate matrix coefficients at the time derivative is discussed. Examples of such systems are the linearized Navier-Stokes system, the system of Rossby waves, the Sobolev system and the system of internal waves. Since the matrix of coefficients is degenerated, the system of equations fail to be of Cauchy-Kovalevskaya type, therefore the boundary value problems have peculiarities. For the Sobolev system, the system of internal waves and the system of gravitational gyroscopical waves for Boussinesq approximation, solvability and well-posedness in weighted Sobolev space, if the Lopatinskii condition holds, is shown.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 918053
zbMATH Keywords: non-Cauchy-Kovalevskaya-type system
zbMATH Keywords: integro-differential systems
zbMATH Keywords: degenerate matrix coefficients
zbMATH Keywords: Sobolev system
zbMATH Keywords: system of internal waves
zbMATH Keywords: gravitational gyroscopical waves
zbMATH Keywords: well-posedness in weighted Sobolev space
zbMATH Keywords: Lopatinskii condition
author: G. V. Demidenko
author: I. I. Matveeva
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 918053