Abstract
This paper deals with an inverse problem of determining a space-dependent source coefficient in the 2D/3D advection-dispersion equation with final observations using the variational adjoint method. Data compatibility for the inverse problem is analyzed by which an admissible set for the unknowns is induced. With the aid of an adjoint problem, a bilinear functional based on the variational identity is set forth with which a norm for the unknown is well-defined under suitable conditions, and then a conditional Lipschitz stability for the inverse problem is established. Furthermore, numerical inversions with random noisy data are performed using the optimal perturbation algorithm, and the inversion solutions give good approximations to the exact solution as the noise level goes to small.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11371231
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11071148
Funding source: Natural Science Foundation of Shandong Province
Award Identifier / Grant number: ZR2011AQ014
Funding statement: This work is partially supported by National Natural Science Foundation of China (No. 11371231, No. 11071148), and Natural Science Foundation of Shandong Province (No. ZR2011AQ014).
Acknowledgements
The authors thank the anonymous referees and the editor for their valuable and suggestive comments.
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© 2017 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- A functional Hodrick–Prescott filter
- On the peakon inverse problem for the Degasperis–Procesi equation
- Recovery of harmonic functions from partial boundary data respecting internal pointwise values
- Inverse spectral problems of transmission eigenvalue problem for anisotropic media with spherical symmetry assumptions
- An inverse problem for a nonlinear diffusion equation with time-fractional derivative
- Imaging of complex-valued tensors for two-dimensional Maxwell’s equations
- Direct and inverse source problems for a space fractional advection dispersion equation
- A conditional Lipschitz stability for determining a space-dependent source coefficient in the 2D/3D advection-dispersion equation
- Inverse transmission eigenvalue problems with the twin-dense nodal subset
- Stability of the inverse boundary value problem for the biharmonic operator: Logarithmic estimates
Artikel in diesem Heft
- Frontmatter
- A functional Hodrick–Prescott filter
- On the peakon inverse problem for the Degasperis–Procesi equation
- Recovery of harmonic functions from partial boundary data respecting internal pointwise values
- Inverse spectral problems of transmission eigenvalue problem for anisotropic media with spherical symmetry assumptions
- An inverse problem for a nonlinear diffusion equation with time-fractional derivative
- Imaging of complex-valued tensors for two-dimensional Maxwell’s equations
- Direct and inverse source problems for a space fractional advection dispersion equation
- A conditional Lipschitz stability for determining a space-dependent source coefficient in the 2D/3D advection-dispersion equation
- Inverse transmission eigenvalue problems with the twin-dense nodal subset
- Stability of the inverse boundary value problem for the biharmonic operator: Logarithmic estimates