Existence and uniqueness of solutions of a mixed problem for a symmetric hyperbolic system with discontinuous coefficients
type: Item
instance of: scholarly article
title: Existence and uniqueness of solutions of a mixed problem for a symmetric hyperbolic system with discontinuous coefficients
zbMATH Open document ID: 0562.35056
DOI: 10.1007/BF02844613
author: Ettore Santi
publication date: 1984-01-01T00:00:00Z
review text: The author considers in the cylindrical space-time domain \(\Omega\) \(\times [0,T]\) the first order linear differential system \((1)\quad (\partial /\partial t)(Au)+\sum^{n}_{i=1}A^ i\partial u/\partial x_ i=f,\) where the \(m\times m\) matrix A is symmetric and coercive and the \(m\times m\) matrices \(A^ i\) are symmetric, together with the initial condition (2) \(u(x,0)=h(x)\), \(x\in \Omega\), and with conservative boundary conditions (3) \({\mathfrak B}u=0\) on \(\partial \Omega \times [0,T]\). - The entries of the matrix A are bounded but may be strongly irregular whereas the entries of the matrices \(A^ i(i=1,...,n)\) are constant. With the aid of well-known results of the general theory of mixed first- order problems with regular coefficients, the author proves existence and uniqueness theorems for the weak \(L^ 2\)-solutions of problem (1)-(2)- (3). - On this ground a uniqueness theorem is also proved for a nonlinear variant of the same problem.
Mathematics Subject Classification ID: 35L50
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 3895531
zbMATH Keywords: first order linear differential system
zbMATH Keywords: symmetric and coercive
zbMATH Keywords: conservative boundary conditions
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: weak \(L^ 2\)- solutions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02844613
OpenAlex ID: W1978205707
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 3895531