6 citations · 21 across the 17 of their papers we have counts for
18 papers
Optimality Conditions for Control Systems Governed by Monotone Stochastic Evolution Equations
Ioana Ciotir, Nicolas Forcadel, Piero Visconti +1
We study a class of optimal control problems governed by nonlinear stochastic equations of monotone type under certain coercivity and linear growth conditions. We give first order…
Beyond uniqueness: Relaxation calculus of junction conditions for coercive Hamilton-Jacobi equations
Nicolas Forcadel, Regis Monneau
A junction is a particular network given by the collection of half lines glued together at the origin. On such a junction, we consider evolutive Hamilton-Jac…
Limits of non-local approximations to the Eikonal equation on manifolds
Jalal M. Fadili, Nicolas Forcadel, Rita Zantout
In this paper, we consider a non-local approximation of the time-dependent Eikonal equation defined on a Riemannian manifold. We show that the local and the non-local problems are…
Germs for scalar conservation laws: the Hamilton-Jacobi equation point of view
Nicolas Forcadel, Cyril Imbert, Regis Monneau
We prove that the entropy solution to a scalar conservation law posed on the real line with a flux that is discontinuous at one point (in the space variable) coincides with the der…
The twin blow-up method for Hamilton-Jacobi equations in higher dimension
Nicolas Forcadel, Cyril Imbert, Regis Monneau
In this paper, we show how to extend the twin blow-up method recently developped by the authors (Comptes Rendus. Math., 2024), in order to obtain a new comparison principle for an…
A class of germs arising from homogenization in traffic flow on junctions
Pierre Cardaliaguet, Nicolas Forcadel, Regis Monneau
We consider traffic flows described by conservation laws. We study a 2:1 junction (with two incoming roads and one outgoing road) or a 1:2 junction (with one incoming road and two…
Conservation law and Hamilton-Jacobi equations on a junction: the convex case
Pierre Cardaliaguet, Nicolas Forcadel, Theo Girard +1
The goal of this paper is to study the link between the solution to an Hamilton-Jacobi (HJ) equation and the solution to a Scalar Conservation Law (SCL) on a special network. When…
Coercive Hamilton-Jacobi equations in domains: the twin blow-ups method
Nicolas Forcadel, Cyril Imbert, Regis Monneau
In this note, we consider an evolution coercive Hamilton-Jacobi equation posed in a domain and supplemented with a boundary condition. We are interested in proving a comparison pri…
Non-convex coercive Hamilton-Jacobi equations: Guerand's relaxation revisited
Nicolas Forcadel, Cyril Imbert, Regis Monneau
This work is concerned with Hamilton-Jacobi equations of evolution type posed in domains and supplemented with boundary conditions. Hamiltonians are coercive but are neither convex…
Microscopic derivation of a traffic flow model with a bifurcation
P Cardaliaguet, N Forcadel
The goal of the paper is a rigorous derivation of a macroscopic traffic flow model with a bifurcation or a local perturbation from a microscopic one. The microscopic model is a sim…
Limits and consistency of non-local and graph approximations to the Eikonal equation
Jalal Fadili, Nicolas Forcadel, Thi Tuyen Nguyen +1
In this paper, we study a non-local approximation of the time-dependent (local) Eikonal equation with Dirichlet-type boundary conditions, where the kernel in the non-local problem…
Stochastic homogenization of Hamilton-Jacobi equations on a junction
Nicolas Forcadel, Fayad Rim, Ibrahim Hassan
We consider the specified stochastic homogenization of first order evolutive Hamilton-Jacobi equations on a very simple junction, i.e the real line with a junction at the origin. F…
From heterogeneous microscopic traffic flow models to macroscopic models
Pierre Cardaliaguet, Nicolas Forcadel
The goal of this paper is to derive rigorously macroscopic traffic flow models from microscopic models. More precisely, for the microscopic models, we consider follow-the-leader ty…
A semi-Lagrangian scheme for Hamilton-Jacobi equations on networks with application to traffic flow models
Elisabetta Carlini, Adriano Festa, Nicolas Forcadel
We present a semi-Lagrangian scheme for the approximation of a class of Hamilton-Jacobi-Bellman equations on networks. The scheme is explicit and stable under some technical condit…
Steady state and long time convergence of spirals moving by forced mean curvature motion
Nicolas Forcadel, Cyril Imbert, Régis Monneau
In this paper, we prove the existence and uniqueness of a "steady" spiral moving with forced mean curvature motion. This spiral has a stationary shape and rotates with constant ang…
Existence and uniqueness of traveling wave for accelerated Frenkel-Kontorova model
Nicolas Forcadel, Amin Ghorbel, Sonda Walha
In this paper, we study the existence and uniqueness of traveling wave solution for the accelerated Frenkel-Kontorova model. This model consists in a system of ODE that describes t…
Uniqueness and existence of spirals moving by forced mean curvature motion
Nicolas Forcadel, Cyril Imbert, Régis Monneau
In this paper, we study the motion of spirals by mean curvature type motion in the (two dimensional) plane. Our motivation comes from dislocation dynamics; in this context, spirals…
Homogenization of accelerated Frenkel-Kontorova models with types of particles
Nicolas Forcadel, Cyril Imbert, Régis Monneau
We consider systems of ODEs that describe the dynamics of particles. Each particle satisfies a Newton law (including the acceleration term) where the force is created by the intera…