Advertisement

On the Various Formulations of the One-Dimensional Inverse Problem for the Telegraph Equation

  • A. S. Blagoveshchenskii
Part of the Topics in Mathematical Physics book series (TOMP, volume 4)

Abstract

In this note we establish the equivalence of two formulations of the inverse problem on finding the unknown coefficient q(z) in the telegraph equation
$$ {u_{tt}} = \Delta u + q(z)u,\;(x,y) \in {R_2},\;z > $$
(1)
if it is known that u(x, y, z, t) is a solution of equation (1) satisfying the conditions
$$ u{|_{t > 0}} \equiv 0$$
(2)
$$ {u_z}{|_{z = 0}} = \partial (x,y,t)$$
(3)
. Suppose that for z = 0 u is the function f (x, y, t)
$$ u{|_{z = 0}} = f(x,y,t)$$
(4)
certain properties of which are given.

Keywords

Nauk SSSR Wave Propagation Inverse Problem Mathematical Physic EQUA TION 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Literature Cited

  1. 1.
    V. G. Romanov, “The one-dimensional inverse problem for the telegraph equation,” Differentsial’nye Uravneniya, Vol. 4, No. 1 (1968).Google Scholar
  2. 2.
    M. G. Krein, “On a certain method of effective solution of the inverse problem,” Dokl. Akad. Nauk SSSR, Vol. 94, No. 6 (1954).Google Scholar
  3. 3.
    A. S. Alekseev, “Some inverse problems in the theory of wave propagation I, II,” Izv. Akad. Nauk SSSR, Ser. Geofiz., No. 11 (1962).Google Scholar
  4. 4.
    A. S. Blagoveshchenskii, “On the inverse problem in the theory of propagation of seismic waves,” in: Topics in Mathematical Physics, Vol. 1, Consultants Bureau, New York (1967).Google Scholar

Copyright information

© Consultants Bureau, New York 1971

Authors and Affiliations

  • A. S. Blagoveshchenskii

There are no affiliations available

Personalised recommendations