The geometry of convex surfaces and inverse problems of scattering theory

1994 ◽  
Vol 35 (5) ◽  
pp. 845-862
Author(s):  
Yu. E. Anikonov ◽  
V. N. Stepanov
Keyword(s):  
Inverse Problems ◽  
Scattering Theory ◽  
Convex Surfaces

Direct and inverse problems of wave propagation through a one-dimensional inhomogeneous medium

1999 ◽  
Vol 10 (1) ◽  
pp. 79-96 ◽  
Author(s):  
A. S. ALEKSEEV ◽  
V. S. BELONOSOV
Keyword(s):  
Inverse Problems ◽  
Scattering Theory ◽  
Wave Process ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Direct And Inverse Problems ◽  
One Dimensional ◽  
Initial Boundary Value ◽  
Theoretical Results ◽  
Transmission And Reflection

This paper deals with a wave process induced by an acoustic impulse in a vertically inhomogeneous half-space. The solvability of the corresponding direct initial boundary value problem is proved. We also consider a class of one-dimensional inverse problems including, in particular, the classical inverse problem of the scattering theory, the transmission and reflection problems of seismology, etc. It is shown that all these inverse problems are equivalent in a certain sense, and therefore can be solved by identical methods. Theoretical results are illustrated by numerical examples.

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