Selçuk Journal of Applied Mathematics

 Selçuk Journal of
  Applied Mathematics

  Winter-Spring, 2001
  Volume  2
  Number 1

Research Center of 
  Applied Mathematics

 SJAM Winter-Spring 2001, Volume 2 - Number 1

A local inverse problem for Hamilton-Jacobi equation
Reconstruction of Riemannian metric

I.V. Golubyatnikov 1* , Hilmi H. Hacisalihouğlu 2*

1 Novosibirsk State Technical University, Novosibirsk, Russia

2 Ankara University, Ankara, Turkey

Received: January 23, 2001

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).

Key words
Inverse problem, hamiltonian, Hamilton system, trajectories

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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