Spectral Theory and Wave Processes pp 35-36 | Cite as

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

Chapter

## 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 if it is known that u(x, y, z, t) is a solution of equation (1) satisfying the conditions . Suppose that for z = 0 u is the function certain properties of which are given.

$$ {u_{tt}} = \Delta u + q(z)u,\;(x,y) \in {R_2},\;z > $$

(1)

$$ u{|_{t > 0}} \equiv 0$$

(2)

$$ {u_z}{|_{z = 0}} = \partial (x,y,t)$$

(3)

*f*(x, y, t)$$ u{|_{z = 0}} = f(x,y,t)$$

(4)

## Keywords

Nauk SSSR Wave Propagation Inverse Problem Mathematical Physic EQUA TION
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## Literature Cited

- 1.V. G. Romanov, “The one-dimensional inverse problem for the telegraph equation,” Differentsial’nye Uravneniya, Vol. 4, No. 1 (1968).Google Scholar
- 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.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.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