Inverse Problems for Partial Differential Equations pp 184-217 | Cite as

Hyperbolic Problems

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• Victor Isakov

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Part of the Applied Mathematical Sciences book series (AMS, volume 127)

Abstract

In this chapter we are interested in finding coefficients of the second-order hyperbolic operator

$$ {a_0}\partial _t^2u + Au = f\;in\;Q = \Omega \times (0,T) $$

(8.0.1)

given the initial data

$$ u = {u_0},\;{\partial _t}u = {u_1}\;on\;\Omega \times \left\{ 0 \right\}, $$

(8.0.2)

the Neumann lateral data

$$ av \cdot \nabla u = h\;{\text{on}}\;{\Gamma _1} \times (0,T), $$

(8.0.3)

and the additional lateral data

$$ u = g\;{\text{on}}\;{\Gamma _0} \times (0,T). $$

(8.0.4)

Keywords

Inverse Problem Hyperbolic Equation Boundary Control Cauchy Data Inverse Spectral Problem 

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.

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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

• Victor Isakov
  • 1

1. 1.Department of Mathematics and StatisticsThe Wichita State UniversityWichitaUSA