Differential and Integral Equations

A symmetric positive system with nonuniformly characteristic boundary

Paolo Secchi

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Abstract

We study linear symmetric positive systems under maximal nonnegative boundary conditions. First we consider the noncharacteristic boundary and nonhomogeneous boundary conditions; in this case we give sufficient conditions on the boundary data in order to have $L^2$ and $H^1$ solutions. The inhomogeneous boundary data are treated directly with the advantage of requiring minimal regularity assumptions. Secondly we consider a boundary value problem with boundary matrix not of constant rank. We assume that the boundary is divided in two parts by an embedded manifold which is the intersection of the reference domain and a noncharacteristic hypersurface. The boundary matrix is negative definite on one side of the boundary with respect to the embedded manifold and is positive semi-definite on the other one. Using also the results of the first part, we discuss the existence of regular solutions.

Article information

Source
Differential Integral Equations, Volume 11, Number 4 (1998), 605-621.

Dates
First available in Project Euclid: 30 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367341036

Mathematical Reviews number (MathSciNet)
MR1666202

Zentralblatt MATH identifier
1131.35324

Subjects
Primary: 35J55
Secondary: 35F15: Boundary value problems for linear first-order equations 35L50: Initial-boundary value problems for first-order hyperbolic systems

Citation

Secchi, Paolo. A symmetric positive system with nonuniformly characteristic boundary. Differential Integral Equations 11 (1998), no. 4, 605--621. https://projecteuclid.org/euclid.die/1367341036


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