• Publications
  • Influence
On selection dynamics for competitive interactions
  • P. Jabin, G. Raoul
  • Mathematics, Medicine
  • Journal of mathematical biology
  • 1 September 2011
In this paper, we are interested in an integro-differential model that describe the evolution of a population structured with respect to a continuous trait. Under some assumption, we are able to findExpand
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Line-energy Ginzburg-Landau models: zero-energy states
We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states ofExpand
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On the rate of convergence to equilibrium in the Becker–Döring equations
Abstract We provide an explicit rate of convergence to equilibrium for solutions of the Becker–Doring equations using the energy/energy-dissipation relation. The main difficulty is the structure ofExpand
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Particles approximations of Vlasov equations with singular forces : Propagation of chaos
We obtain the mean field limit and the propagation of chaos for a system of particles interacting with a singular interaction force of the type $1/|x|^\alpha$, with $\alpha <1$ in dimension $d \geqExpand
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Clustering and asymptotic behavior in opinion formation
Abstract We investigate the long time behavior of models of opinion formation. We consider the case of compactly supported interactions between agents which are also non-symmetric, including forExpand
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Regularity in kinetic formulations via averaging lemmas
We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particularExpand
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Global Existence of Weak Solutions for Compresssible Navier--Stokes Equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor
We prove global existence of appropriate weak solutions for the compressible Navier--Stokes equations for more general stress tensor than those covered by P.-L. Lions and E. Feireisl's theory. MoreExpand
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On selection dynamics for continuous structured populations
In this paper, we provide results about the long time behavior of integrodifferential equations appearing in the study of populations structured with respect to a quantitative (continuous) trait,Expand
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A review of the mean field limits for Vlasov equations
We review some classical and more recent results on the mean field limit and propagation of chaos for systems of many particles, leading to Vlasov or macroscopic equations.
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N-particles Approximation of the Vlasov Equations with Singular Potential
AbstractWe prove the convergence in any time interval of a point-particle approximation of the Vlasov equation by particles initially equally separated for a force in 1/|x|α, with $$\alpha \leqq 1$$.Expand
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