Fifth Mississippi State Conference on Differential Equations and
Computational Simulations,
Electron. J. Diff. Eqns., Conf. 10, 2003, pp. 153161.
A selfadjoint hyperbolic boundaryvalue problem
Nezam Iraniparast
Abstract:
We consider the eigenvalue wave equation
subject to
,
where
, is a function of
,
with
.
In the characteristic triangle
we impose a boundary condition along characteristics so that
The parameters
and
are arbitrary except for the condition that
they are not both zero. The two vectors
and
are the exterior unit normals
to the characteristic boundaries and
,
are the normal derivatives in those directions. When
we will show that the above characteristic boundary value problem
has real, discrete eigenvalues and corresponding eigenfunctions
that are complete and orthogonal in
.
We will also investigate the case where
is an arbitrary continuous function in
.
Published February 28, 2003.
Subject classifications: 35L05, 35L20, 35P99.
Key words: Characteristics, eigenvalues,
eigenfunctions, Green's function, Fredholm alternative.
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Nezam Iraniparast
Department of Mathematics
Western Kentucky University
Email: nezam.iraniparast@wku.edu

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