Geodesic
The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion
Applications of Mathematics, Tome 67 (2022) no. 1, pp. 1-20.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary of the subregion the solution satisfies a generalized impedance boundary condition. This boundary condition is given by a second order spatial differential operator imposed on the boundary. A generalized impedance boundary condition can be used to model corrosion and delimitation. The well-posedness for the direct problem is established where the Laplace transform is used to study the time dependent boundary value problem. The inverse impedance problem of determining the parameters from the Cauchy data is also studied provided the boundary of the subregion is known. The uniqueness of recovering the boundary parameters from the Neumann to Dirichlet mapping is proven.
DOI : 10.21136/AM.2021.0107-20
Classification : 35R11, 35R30
Keywords: fractional diffusion; Laplace transform; inverse impedance problem 
@article{10_21136_AM_2021_0107_20,
     author = {Harris, Isaac},
     title = {The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion},
     journal = {Applications of Mathematics},
     pages = {1--20},
     publisher = {mathdoc},
     volume = {67},
     number = {1},
     year = {2022},
     doi = {10.21136/AM.2021.0107-20},
     mrnumber = {4392402},
     zbl = {07478514},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0107-20/}
}
TY  - JOUR
AU  - Harris, Isaac
TI  - The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion
JO  - Applications of Mathematics
PY  - 2022
SP  - 1
EP  - 20
VL  - 67
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0107-20/
DO  - 10.21136/AM.2021.0107-20
LA  - en
ID  - 10_21136_AM_2021_0107_20
ER  - 
%0 Journal Article
%A Harris, Isaac
%T The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion
%J Applications of Mathematics
%D 2022
%P 1-20
%V 67
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0107-20/
%R 10.21136/AM.2021.0107-20
%G en
%F 10_21136_AM_2021_0107_20
Harris, Isaac. The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion. Applications of Mathematics, Tome 67 (2022) no. 1, pp. 1-20. doi : 10.21136/AM.2021.0107-20. http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0107-20/

Cité par Sources :