Inverse Problems for Hyperbolic Equations

Alemdar Hasanov Hasanoğlu and Vladimir G. Romanov
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Alemdar Hasanov Hasanoğlu: University of Kocaeli, Department of Mathematics
Vladimir G. Romanov: Sobolev Institute of Mathematics

Chapter Chapter 4 in Introduction to Inverse Problems for Differential Equations, 2021, pp 129-150 from Springer

Abstract: Abstract In the first part of this chapter we study two inverse source problems related to the second order hyperbolic equations u tt − u xx = ρ(x, t)g(t) and u tt − u xx = ρ(x, t)φ(x) for the quarter plane ℝ + 2 = { ( x , t ) | x > 0 , t > 0 } $$\mathbb {R}^2_+=\{(x,t)|\, x>0, t>0\}$$ , with Dirichlet type measured output f(t) := u(x, t)|x=0. The time-dependent source g(t) and the spacewise-dependent source φ(x) are assumed to be unknown in these inverse problems.

Date: 2021
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DOI: 10.1007/978-3-030-79427-9_4

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