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An inverse source problem for a damped wave equation with memory
-
Lukáš Šeliga
and
Marián Slodička
Published/Copyright:
January 15, 2015
Abstract
Inverse problem of identifying the unknown spacewise dependent source f(x) in a nonlinear damped wave equation with a memory term is investigated. The missing coefficient f(x) is reconstructed from the final time observation u(x,T) = ψT(x). Uniqueness of a solution to the inverse source problem is proved. We also propose a Landweber-type algorithm for reconstruction. Convergence of approximations towards the exact solution is established for a linear equation.
Keywords: Inverse source problem; damped wave equation
MSC: 65M32
Funding source: Belgian Science Policy
Award Identifier / Grant number: IAP P7/02
Received: 2014-3-26
Revised: 2014-11-14
Accepted: 2014-12-12
Published Online: 2015-1-15
Published in Print: 2016-4-1
© 2016 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Preface
- In celebration of the 60th birthday of Professor Alemdar Hasanoğlu (Hasanov)
- An inverse source problem for a damped wave equation with memory
- On the Cauchy problem for semilinear elliptic equations
- A unified approach to convergence rates for ℓ1-regularization and lacking sparsity
- Regularization of ill-posed problems by using stabilizers in the form of the total variation of a function and its derivatives
- Numerical testing in determination of sound speed from a part of boundary by the BC-method
- Inverse determination of spatially varying material coefficients in solid objects
- Determination of the initial condition in parabolic equations from boundary observations
