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

Abstract

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.

Keywords:

• Stability
• inverse problems
• tumor growth model
• Carleman estimate

2010 Mathematics Subject Classifications:

• 35K05
• 35R30
• 35K61
• 35Q92

Acknowledgments

The authors would like to thank anonymous referees for invaluable comments which led to this improved version.

Disclosure statement

No potential conflict of interest was reported by the author(s).