The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion

Isaac Harris

Applications of Mathematics (2022)

  • Volume: 67, Issue: 1, page 1-20
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Harris, Isaac. "The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion." Applications of Mathematics 67.1 (2022): 1-20. <http://eudml.org/doc/297574>.

@article{Harris2022,
abstract = {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.},
author = {Harris, Isaac},
journal = {Applications of Mathematics},
keywords = {fractional diffusion; Laplace transform; inverse impedance problem},
language = {eng},
number = {1},
pages = {1-20},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion},
url = {http://eudml.org/doc/297574},
volume = {67},
year = {2022},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 1
SP - 1
EP - 20
AB - 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.
LA - eng
KW - fractional diffusion; Laplace transform; inverse impedance problem
UR - http://eudml.org/doc/297574
ER -

References

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