Hyperbolic Problems

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)