Page 456 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 456
NALYSIS, CONTROL AND INVERSE PROBLEMS FOR PARTIAL DIFFERENTIAL
EQUATIONS (MS-22)
Optimal Control in Poroelasticity
Lorena Bociu, lvbociu@ncsu.edu
NC State University, United States
Coauthor: Sarah Strikwerda
In this talk we address optimal control problems subject to fluid flows through deformable,
porous media. In particular, we focus on quadratic poroelasticity control problems, with both
distributed and boundary controls, and prove existence and uniqueness of optimal control. Fur-
thermore, we derive the first order necessary optimality conditions. These problems have im-
portant biological and biomechanical applications. For example, optimizing the pressure of
the flow and investigating the influence and control of pertinent biological parameters are rele-
vant in ocular tissue perfusion and its relation to the development of ocular neurodegenerative
diseases such as glaucoma.
The Calderón problem with corrupted data
Pedro Caro, pcaro@bcamath.org
Basque Center for Applied Mathematics, Spain
The inverse Calderón problem consists in determining the conductivity inside a medium by
electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-
to-Neumann map and, therefore, one usually assumes the data to be given by such map. This
situation corresponds to having access to infinite-precision measurements, which is unrealistic.
In this talk, I will consider the Calderón problem assuming data to contain measurement errors
and provide formulas to reconstruct the conductivity and its normal derivative on the surface
(joint work with Andoni García). I will also present similar results for Maxwell’s equations
(joint work with Ru-Yu Lai, Yi-Hsuan Lin, Ting Zhou ). When modelling errors in these two
different frameworks, one realizes the existence of certain freedom that yields different recon-
struction formulas. To understand the whole picture of what is going on, we will rewrite the
problem in a different setting, which will bring us to analyse the observational limit of wave
packets with noisy measurements (joint work with Cristóbal J. Meroño).
Stable determination of polygonal and polyhedral interfaces from
boundary measurements
Elisa Francini, elisa.francini@unifi.it
Università di Firenze, Italy
I will present some results concerning Lipschitz stability in the determination of polygonal and
polyhedral inclusions from the Dirichlet to Neumann map.
454
EQUATIONS (MS-22)
Optimal Control in Poroelasticity
Lorena Bociu, lvbociu@ncsu.edu
NC State University, United States
Coauthor: Sarah Strikwerda
In this talk we address optimal control problems subject to fluid flows through deformable,
porous media. In particular, we focus on quadratic poroelasticity control problems, with both
distributed and boundary controls, and prove existence and uniqueness of optimal control. Fur-
thermore, we derive the first order necessary optimality conditions. These problems have im-
portant biological and biomechanical applications. For example, optimizing the pressure of
the flow and investigating the influence and control of pertinent biological parameters are rele-
vant in ocular tissue perfusion and its relation to the development of ocular neurodegenerative
diseases such as glaucoma.
The Calderón problem with corrupted data
Pedro Caro, pcaro@bcamath.org
Basque Center for Applied Mathematics, Spain
The inverse Calderón problem consists in determining the conductivity inside a medium by
electrical measurements on its surface. Ideally, these measurements determine the Dirichlet-
to-Neumann map and, therefore, one usually assumes the data to be given by such map. This
situation corresponds to having access to infinite-precision measurements, which is unrealistic.
In this talk, I will consider the Calderón problem assuming data to contain measurement errors
and provide formulas to reconstruct the conductivity and its normal derivative on the surface
(joint work with Andoni García). I will also present similar results for Maxwell’s equations
(joint work with Ru-Yu Lai, Yi-Hsuan Lin, Ting Zhou ). When modelling errors in these two
different frameworks, one realizes the existence of certain freedom that yields different recon-
struction formulas. To understand the whole picture of what is going on, we will rewrite the
problem in a different setting, which will bring us to analyse the observational limit of wave
packets with noisy measurements (joint work with Cristóbal J. Meroño).
Stable determination of polygonal and polyhedral interfaces from
boundary measurements
Elisa Francini, elisa.francini@unifi.it
Università di Firenze, Italy
I will present some results concerning Lipschitz stability in the determination of polygonal and
polyhedral inclusions from the Dirichlet to Neumann map.
454
