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One
Dimensional Inverse Problems
of Elasticity, Electromagnetoelasticity,
Thermoelasticity, Viscoelasticity
This project deals with the initial boundary value problems
and Cauchy problems for differential equations systems of
anisotropic
elasticity, electromagnetoelasticity, thermoelasticity,
viscoelasticity. These differential equations systems are
considered
in the whole three-dimensional space or in some regions of the
three-dimensional space if it does not consider the time
variable.
The coefficients of these differential equations systems are
supposed
to be the smooth or piecewise smooth functions depending on one
variable only. For example, this variable for elasticity medium
in
three-dimensional half space is a depht. The coefficients of
these
systems are the characteristics of inhomogeneous (vertical or
radial
inhomogeneous) media in which the wave processes propagate. These
one-dimensional inverse problems consist in finding all
coeficients
of these differential equations systems or part of them if it is
given
the additional information respect to solutions of the Cauchy or
initial boundary value problems for these systems with the
special
initial data, boundary conditions and special right-hand sides of
these systems.The additional information for inverse problems
solving is the dynamic of the wave fields in the fixed point of
the
space or on the boundary of the limited regions at the times
belonging
to the given limited interval.
The results of the investigation will consist in uniqueness,
stability
estimates, existence theorems and algorithms of their solving.
This research continues the investigation started in the
monographies
Lavrent'ev, Reznitskaya, Yakhno (1986), Yakhno (1994).
References
Lavrent'ev M.M., Reznitskaya K.G., Yakhno V.G.(1986)
One-dimensional Inverse
Problems of Mathematical Physics, American Mathematical Society
Translations, series 2, Vol.130.
Yakhno V.G. (1990) Inverse Problems for Differential Equtions of
Elasticity
Nauka, Novosibirsk (in Russian).
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