An inverse problem for an elliptic equation in a spherical domain

2021 ◽  
pp. 1-8
Author(s):  
Doo-Sung Lee
Keyword(s):  
Inverse Problem ◽  
Elliptic Equation ◽  
Spherical Domain

scholarly journals AN INVERSE BOUNDARY VALUE PROBLEM FOR A SECOND ORDER ELLIPTIC EQUATION IN A RECTANGLE

2014 ◽  
Vol 19 (2) ◽  
pp. 241-256 ◽  
Author(s):  
Yashar T. Mehraliyev ◽  
Fatma Kanca
Keyword(s):  
Inverse Problem ◽  
Elliptic Equation ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Order Elliptic Equation ◽  
Inverse Boundary ◽  
Numerical Tests ◽  
Second Order Elliptic Equation

In this paper, the inverse problem of finding a coefficient in a second order elliptic equation is investigated. The conditions for the existence and uniqueness of the classical solution of the problem under consideration are established. Numerical tests using the finite-difference scheme combined with an iteration method is presented and the sensitivity of this scheme with respect to noisy overdetermination data is illustrated.

An inverse problem for an elliptic equation

2016 ◽  
Vol 95 (4) ◽  
pp. 919-929 ◽  
Author(s):  
Doo-Sung Lee
Keyword(s):  
Inverse Problem ◽  
Elliptic Equation

Identification of point sources in an elliptic equation from interior measurements: Application to a seawater intrusion problem

2019 ◽  
Vol 27 (4) ◽  
pp. 559-574 ◽  
Author(s):  
Abdellatif El Badia ◽  
Ahmad El Hajj ◽  
Mustapha Jazar ◽  
Hayat Moustafa
Keyword(s):  
Inverse Problem ◽  
Elliptic Equation ◽  
Cost Function ◽  
Seawater Intrusion ◽  
Rectangular Domain ◽  
Numerical Results ◽  
Point Sources ◽  
Inverse Source Problem

Abstract This paper deals with an inverse source problem for an elliptic equation, using interior measurements. Its motivation lies in the seawater intrusion phenomenon, where we are interested in identifying point sources representing illegal wells. A cost function transforming our inverse problem into an optimization one is proposed, and numerical results are performed for a rectangular domain.

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