Inverse problem for a Cahn-Hilliard type system modeling tumor growth

In this paper, we address an inverse problem of reconstructing a space-dependent semilinear coefficient in the tumor growth model described by a system of semilinear partial differential equations (PDEs) with Dirichlet boundary condition using boundary-type measurement. We establish a new higher ord...

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Bibliographic Details
Published inApplicable analysis Vol. 101; no. 3; pp. 858 - 890
Main Authors Sakthivel, K., Arivazhagan, A., Barani Balan, N.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 11.02.2022
Taylor & Francis Ltd
Subjects
Boundary conditions
Carleman estimate
Dirichlet problem
Growth models
Inverse problems
Nonlinear systems
Partial differential equations
Stability
tumor growth model
Tumors
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Summary:In this paper, we address an inverse problem of reconstructing a space-dependent semilinear coefficient in the tumor growth model described by a system of semilinear partial differential equations (PDEs) with Dirichlet boundary condition using boundary-type measurement. We establish a new higher order weighted Carleman estimate for the given system with the help of Dirichlet boundary conditions. By deriving a suitable regularity of solutions for this nonlinear system of PDEs and the new Carleman estimate, we prove Lipschitz-type stability for the tumor growth model.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2020.1761016