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Mickaël D. Chekroun

  1. Climate dynamics and fluid mechanics: Natural variability and related uncertainties.

    Wed, 06/16/2010 - 15:01 — SomNambul
    Authors: Mickaël D. Chekroun, Michael Ghil, Eric Simonnet
    Subjects: Dynamical Systems
    Abstract

    The purpose of this review-and-research paper is twofold: (i) to review the
    role played in climate dynamics by fluid-dynamical models; and (ii) to
    contribute to the understanding and reduction of the uncertainties in future
    climate-change projections. To illustrate the first point, we focus on the
    large-scale, wind-driven flow of the mid-latitude oceans which contribute in a
    crucial way to Earth's climate, and to changes therein.

  2. Asymptotics of the Coleman-Gurtin model.

    Tue, 06/15/2010 - 15:01 — SomNambul
    Authors: Mickaël D. Chekroun, Francesco Di Plinio, Nathan E. Glatt-Holtz, Vittorino Pata
    Subjects: Analysis of PDEs
    Abstract

    This paper is concerned with the integrodifferential equation $$\partial_t
    u-\Delta u -\int_0^\infty \kappa(s)\Delta u(t-s)\,\d s + \varphi(u)=f$$ arising
    in the Coleman-Gurtin's theory of heat conduction with hereditary memory, in
    presence of a nonlinearity $\varphi$ of critical growth. Rephrasing the
    equation within the history space framework, we prove the existence of global
    and exponential attractors of optimal regularity and finite fractal dimension
    for the related solution semigroup, acting both on the basic weak-energy space
    and on a more regular phase space.

  3. On population resilience to external perturbations.

    Tue, 06/15/2010 - 15:01 — SomNambul
    Authors: Mickaël D. Chekroun, Lionel Roques
    Subjects: Analysis of PDEs
    Abstract

    We study a spatially explicit harvesting model in periodic or bounded
    environments. The model is governed by a parabolic equation with a spatially
    dependent nonlinearity of Kolmogorov--Petrovsky--Piskunov type, and a negative
    external forcing term $-\delta$. Using sub- and supersolution methods and the
    characterization of the first eigenvalue of some linear elliptic operators, we
    obtain existence and nonexistence results as well as results on the number of
    stationary solutions.

  4. Models of population dynamics under the influence of external perturbations: mathematical results.

    Tue, 06/15/2010 - 15:01 — SomNambul
    Authors: Mickaël D. Chekroun, Lionel Roques
    Subjects: Analysis of PDEs
    Abstract

    In this Note, we describe the stationary equilibria and the asymptotic
    behaviour of an heterogeneous logistic reaction-diffusion equation under the
    influence of autonomous or time-periodic forcing terms. We show that the study
    of the asymptotic behaviour in the time-periodic forcing case can be reduced to
    the autonomous one, the last one being described in function of the "size" of
    the external perturbation. Our results can be interpreted in terms of maximal
    sustainable yields from populations. We briefly discuss this last aspect
    through a numerical computation.

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