37 citations · 112 across the 14 of their papers we have counts for
19 papers
Long-time behaviour of an advection-selection equation
Jules Guilberteau, Camille Pouchol, Nastassia Pouradier Duteil
We study the long-time behaviour of the advection-selection equation $$\partial_tn(t,x)+\nabla \cdot \left(f(x)n(t,x)\right)=\left(r(x)-ρ(t)\right)n(t,x),\quad ρ(t)=\int_{\mathbb{R…
A phenotype-structured model for the tumour-immune response
Zineb Kaid, Camille Pouchol, Jean Clairambault
This paper presents a mathematical model for tumour-immune response interactions in the perspective of immunotherapy by immune checkpoint inhibitors ICIs. The model is of the nonlo…
Approximate control of parabolic equations with on-off shape controls by Fenchel duality
Camille Pouchol, Emmanuel Trélat, Christophe Zhang
We consider the internal control of linear parabolic equations through on-off shape controls, i.e., controls of the form with and with a prescri…
Epidemic Models for COVID-19 during the First Wave from February to May 2020: a Methodological Review
Marie Garin, Myrto Limnios, Alice Nicolaï +12
We review epidemiological models for the propagation of the COVID-19 pandemic during the early months of the outbreak: from February to May 2020. The aim is to propose a methodolog…
Solving Abel integral equations by regularisation in Hilbert scales
Cecile Della Valle, Camille Pouchol
Integral operators of Abel type of order a > 0 arise naturally in a large spectrum of physical processes. Their inversion requires care since the resulting inverse problem is ill-p…
Monostability and bistability of biological switches
Nastassia Pouradier Duteil, Jules Guilberteau, Camille Pouchol +1
Cell-fate transition can be modeled by ordinary differential equations (ODEs) which describe the behavior of several molecules in interaction, and for which each stable equilibrium…
Linear inverse problems with nonnegativity constraints: singularity of optimisers
Camille Pouchol, Olivier Verdier
We look at continuum solutions in optimisation problems associated to linear inverse problems with non-negativity constraint . We focus on the case where the noi…
ML-EM algorithm with known continuous movement model
Camille Pouchol, Olivier Verdier
In Positron Emission Tomography, movement leads to blurry reconstructions when not accounted for. Whether known a priori or estimated jointly to reconstruction, motion models are i…
The ML-EM algorithm in continuum: sparse measure solutions
Camille Pouchol, Olivier Verdier
Linear inverse problems with Poisson noise and non-negative unknown are ubiquitous in applications, for instance in Positron Emission Tomography (PET) in medical…
Spatiotemporal PET reconstruction using ML-EM with learned diffeomorphic deformation
Ozan Öktem, Camille Pouchol, Olivier Verdier
Patient movement in emission tomography deteriorates reconstruction quality because of motion blur. Gating the data improves the situation somewhat: each gate contains a movement p…
Asymptotic analysis of selection-mutation models in the presence of multiple fitness peaks
Tommaso Lorenzi, Camille Pouchol
We study the long-time behaviour of phenotype-structured models describing the evolutionary dynamics of asexual species whose phenotypic fitness landscape is characterised by multi…
Hele-Shaw limit for a system of two reaction-(cross-)diffusion equations for living tissues
Federica Bubba, Benoît Perthame, Camille Pouchol +1
Multiphase mechanical models are now commonly used to describe living tissues including tumour growth. The specific model we study here consists of two equations of mixed parabolic…
A chemotaxis-based explanation of spheroid formation in 3D cultures of breast cancer cells
Federica Bubba, Camille Pouchol, Nathalie Ferrand +4
Three-dimensional cultures of cells are gaining popularity as an in vitro improvement over 2D Petri dishes. In many such experiments, cells have been found to organize in aggregate…
Phase portrait control for 1D monostable and bistable reaction-diffusion equations
Camille Pouchol, Emmanuel Trélat, Enrique Zuazua
We consider the problem of controlling parabolic semilinear equations arising in population dynamics, either in finite time or infinite time. These are the monostable and bistable…
Energy and implicit discretization of the Fokker-Planck and Keller-Segel type equations
Luís Neves de Almeida, Federica Bubba, Benoît Perthame +1
The parabolic-elliptic Keller-Segel equation with sensitivity saturation, because of its pattern formation ability, is a challenge for numerical simulations. We provide two finite-…
On the stability of the state 1 in the non-local Fisher-KPP equation in bounded domains
Camille Pouchol
We consider the non-local Fisher-KPP equation on a bounded domain with Neu-mann boundary conditions. Thanks to a Lyapunov function, we prove that under a general hypothesis on the…
Combination of direct methods and homotopy in numerical optimal control: application to the optimization of chemotherapy in cancer
Antoine Olivier, Camille Pouchol
We consider a state-constrained optimal control problem of a system of two non-local partial-differential equations, which is an extension of the one introduced in a previous work…
Global stability with selection in integro-differential Lotka-Volterra systems modelling trait-structured populations
Camille Pouchol, Emmanuel Trélat
We analyse the asymptotic behaviour of integro-differential equations modelling populations in interaction, all structured by different traits. Interactions are modelled by non…
Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy
Camille Pouchol, Jean Clairambault, Alexander Lorz +1
We consider a system of two coupled integro-differential equations modelling populations of healthy and cancer cells under therapy. Both populations are structured by a phenotypic…