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Selçuk Journal
of
Applied Mathematics
Winter-Spring, 2001
Volume 2
Number 1
Research Center
of
Applied Mathematics
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SJAM
Winter-Spring 2001, Volume 2 - Number 1
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A local inverse problem for Hamilton-Jacobi equation
Reconstruction of Riemannian metric
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I.V.
Golubyatnikov 1* , Hilmi H. Hacisalihouğlu 2* |
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1
Novosibirsk State Technical University, Novosibirsk, Russia
email: deffi2000@mail.ru
2
Ankara University, Ankara, Turkey
email: hacisali@science.ankara.edu.tr
Received: January 23, 2001
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Summary
We
study the uniqueness questions for the inverse problem of
determining hamiltonian H(x,p)= gij (x) pi
pj and a phase function w(x,t) from the
Hamilton-Jacobi equation and the initial-terminal conditions w(x,
t0 ), w(x, t1). Here the unknown functions
gij(x) compose a matrix inverse to that of the
metric tensor. We obtain uniqueness theorems for special classes of
initial-terminal conditions in the cases n =1, n=2 and
in the case of a scalar n×n matrix gij(x).
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Key
words
Inverse problem, hamiltonian, Hamilton system, trajectories
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Mathematics Subject Classification (1991):
33F28,
35R30, 37J99
*
The research was supported by NATO, Grant OUTR.CLG 970357 and by
RFBR Grant No. 99-01-00607.
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Article
in PS format (116 kb) |
Article in
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