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Saada E - One of the best experts on this subject based on the ideXlab platform.

  • Quenched convergence and strong local equilibrium for asymmetric zero-range process with site disorder
    Springer Verlag, 2020
    Co-Authors: Bahadoran Christophe, Mountford T., Ravishankar K., Saada E
    Abstract:

    International audienceWe study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. We prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities, and dynamic local loss of mass at supercritical hydrodynamic densities. Our results do not assume starting from local Gibbs states. As byproducts of these results, we prove convergence of the process from given initial configurations with an asymptotic density of particles to the left of the origin. In particular , we relax the weak convexity assumption of [7, 8] for the escape of mass property. 1 MSC 2010 subject classification: 60K35, 82C22

  • Quenched convergence and strong local equilibrium for asymmetric zero-range process with site disorder
    'Springer Science and Business Media LLC', 2020
    Co-Authors: Bahadoran C., Mountford T., Ravishankar K., Saada E
    Abstract:

    We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. We prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities, and dynamic local loss of mass at supercritical hydrodynamic densities. Our results do not assume starting from local Gibbs states. As byproducts of these results, we prove convergence of the process from given initial configurations with an asymptotic density of particles to the left of the origin. In particular, we relax the weak convexity assumption of Bahadoran et al. (Braz J Probab Stat 29(2):313-335, 2015; Ann Inst Henri Poincare Probab Stat 53(2):766-801, 2017) for the escape of mass property

  • Hydrodynamics In A Condensation Regime: The Disordered Asymmetric Zero-Range Process
    'Institute of Mathematical Statistics', 2020
    Co-Authors: Bahadoran C., Mountford T., Ravishankar K., Saada E
    Abstract:

    We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant

  • Hydrodynamics in a condensation regime: the disordered asymmetric zero-range process
    HAL CCSD, 2020
    Co-Authors: Bahadoran Christophe, Mountford T., Ravishankar K., Saada E
    Abstract:

    International audienceWe study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant

  • Hydrodynamics in a condensation regime: the disordered asymmetric zero-range process
    2019
    Co-Authors: Bahadoran Christophe, Mountford T., Ravishankar K., Saada E
    Abstract:

    We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant.Comment: Annals of Probability, In pres

Veron Laurent - One of the best experts on this subject based on the ideXlab platform.

  • Nonlinear boundary value problems relative to one dimensional heat equation
    Università di Trieste, 2020
    Co-Authors: Veron Laurent
    Abstract:

    22 pages, 16 ref.International audienceWe consider the problem of existence of a solution u to ∂ t u − ∂ xx u = 0 in (0, T) × R + subject to the boundary condition −u x (t, 0) + g(u(t, 0)) = µ on (0, T) where µ is a measure on (0, T) and g a continuous Nondecreasing Function. When p > 1 we study the set of self-similar solutions of ∂ t u − ∂ xx u = 0 in R + × R + such that −u x (t, 0) + u p = 0 on (0, ∞)

  • Nonlinear boundary value problems relative to one dimensional heat equation
    2020
    Co-Authors: Veron Laurent
    Abstract:

    We consider the problem of existence of a solution $u$ to $\partial_t u-\partial_{xx} u = 0$ in $(0,T)\times\mathbb{R}_+$ subject to the boundary condition $-u_x(t,0)+g(u(t,0))=\mu$ on $(0,T)$ where $\mu$ is a measure on $(0,T)$ and $g$ a continuous Nondecreasing Function. When $p>1$ we study the set of self-similar solutions of $\partial_t u-\partial_{xx} u = 0$ in $\mathbb{R}_+\times\mathbb{R}_+$ such that $-u_x(t,0)+u^p=0$ on $(0,\infty)$. At end, we present various extensions to a higher dimensional framework.Comment: 22 pages, 16 ref. Rendiconti dell'Istituto di Matematica dell'Universit{\`a} di Trieste: an International Journal of Mathematics, Universit{\`a} di Trieste, In pres

  • Nonlinear boundary value problems relative to harmonic Functions
    'Elsevier BV', 2020
    Co-Authors: Oussama Boukarabila Y, Veron Laurent
    Abstract:

    International audienceWe study the problem of finding a Function u verifying −∆u = 0 in Ω under the boundary condition ∂u ∂n + g(u) = µ on ∂Ω where Ω ⊂ R N is a smooth domain, n the normal unit outward vector to Ω, µ is a measure on ∂Ω and g a continuous Nondecreasing Function. We give sufficient condition on g for this problem to be solvable for any measure. When g(r) = |r| p−1 r, p > 1, we give conditions in order an isolated singularity on ∂Ω be removable. We also give capacitary conditions on a measure µ in order the problem with g(r) = |r| p−1 r to be solvable for some µ. We also study the isolated singularities of Functions satisfying −∆u = 0 in Ω and ∂u ∂n + g(u) = 0 on ∂Ω \ {0}

  • Weak solutions of semilinear elliptic equations with Leray-Hardy potential and measure data
    'American Institute of Mathematical Sciences (AIMS)', 2019
    Co-Authors: Chen Huyuan, Veron Laurent
    Abstract:

    International audienceWe study existence and stability of solutions of (E 1) −∆u + µ |x| 2 u + g(u) = ν in Ω, u = 0 on ∂Ω, where Ω is a bounded, smooth domain of R N , N ≥ 2, containing the origin, µ ≥ − (N −2) 2 4 is a constant, g is a Nondecreasing Function satisfying some integral growth assumption and ν is a Radon measure on Ω. We show that the situation differs according ν is diffuse or concentrated at the origin. When g is a power we introduce a capacity framework to find necessary and sufficient condition for solvability

  • Weak solutions of semilinear elliptic equations with Leray-Hardy potential and measure data
    2019
    Co-Authors: Veron Laurent, Chen Huyuan
    Abstract:

    We study existence and stability of solutions of (E 1) --$\Delta$u + $\mu$ |x| 2 u + g(u) = $\nu$ in $\Omega$, u = 0 on $\partial$$\Omega$, where $\Omega$ is a bounded, smooth domain of R N , N $\ge$ 2, containing the origin, $\mu$ $\ge$ -- (N --2) 2 4 is a constant, g is a Nondecreasing Function satisfying some integral growth assumption and $\nu$ is a Radon measure on $\Omega$. We show that the situation differs according $\nu$ is diffuse or concentrated at the origin. When g is a power we introduce a capacity framework to find necessary and sufficient condition for solvability

Robin Lindsey - One of the best experts on this subject based on the ideXlab platform.

  • existence uniqueness and trip cost Function properties of user equilibrium in the bottleneck model with multiple user classes
    Transportation Science, 2004
    Co-Authors: Robin Lindsey
    Abstract:

    Under relatively general assumptions a unique deterministic departure-time user equilibrium with a finite departure rate exists in the bottleneck model with drivers who differ in their unit costs of travel time, preferred times of arrival, and schedule delay cost Functions. Existence requires that schedule delay cost Functions be upper semicontinuous with respect to arrival time, and that schedule delay costs decline at a rate smaller than the unit cost of travel time. Uniqueness requires, more restrictively, that schedule delay cost Functions be continuous.Several properties of equilibrium trip cost Functions are derived forn groups of users withN iin groupi. The trip cost of a user in groupi is a Nondecreasing Function of eachN j , but typically rises more quickly with respect toN ithanN j ,j?i. Thus, users experience lower trip costs when they travel with users unlike themselves than with an equal number of users like themselves.

Mountford T. - One of the best experts on this subject based on the ideXlab platform.

  • Quenched convergence and strong local equilibrium for asymmetric zero-range process with site disorder
    Springer Verlag, 2020
    Co-Authors: Bahadoran Christophe, Mountford T., Ravishankar K., Saada E
    Abstract:

    International audienceWe study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. We prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities, and dynamic local loss of mass at supercritical hydrodynamic densities. Our results do not assume starting from local Gibbs states. As byproducts of these results, we prove convergence of the process from given initial configurations with an asymptotic density of particles to the left of the origin. In particular , we relax the weak convexity assumption of [7, 8] for the escape of mass property. 1 MSC 2010 subject classification: 60K35, 82C22

  • Quenched convergence and strong local equilibrium for asymmetric zero-range process with site disorder
    'Springer Science and Business Media LLC', 2020
    Co-Authors: Bahadoran C., Mountford T., Ravishankar K., Saada E
    Abstract:

    We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. We prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities, and dynamic local loss of mass at supercritical hydrodynamic densities. Our results do not assume starting from local Gibbs states. As byproducts of these results, we prove convergence of the process from given initial configurations with an asymptotic density of particles to the left of the origin. In particular, we relax the weak convexity assumption of Bahadoran et al. (Braz J Probab Stat 29(2):313-335, 2015; Ann Inst Henri Poincare Probab Stat 53(2):766-801, 2017) for the escape of mass property

  • Hydrodynamics In A Condensation Regime: The Disordered Asymmetric Zero-Range Process
    'Institute of Mathematical Statistics', 2020
    Co-Authors: Bahadoran C., Mountford T., Ravishankar K., Saada E
    Abstract:

    We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant

  • Hydrodynamics in a condensation regime: the disordered asymmetric zero-range process
    HAL CCSD, 2020
    Co-Authors: Bahadoran Christophe, Mountford T., Ravishankar K., Saada E
    Abstract:

    International audienceWe study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant

  • Hydrodynamics in a condensation regime: the disordered asymmetric zero-range process
    2019
    Co-Authors: Bahadoran Christophe, Mountford T., Ravishankar K., Saada E
    Abstract:

    We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant.Comment: Annals of Probability, In pres

Ravishankar K. - One of the best experts on this subject based on the ideXlab platform.

  • Quenched convergence and strong local equilibrium for asymmetric zero-range process with site disorder
    Springer Verlag, 2020
    Co-Authors: Bahadoran Christophe, Mountford T., Ravishankar K., Saada E
    Abstract:

    International audienceWe study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. We prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities, and dynamic local loss of mass at supercritical hydrodynamic densities. Our results do not assume starting from local Gibbs states. As byproducts of these results, we prove convergence of the process from given initial configurations with an asymptotic density of particles to the left of the origin. In particular , we relax the weak convexity assumption of [7, 8] for the escape of mass property. 1 MSC 2010 subject classification: 60K35, 82C22

  • Quenched convergence and strong local equilibrium for asymmetric zero-range process with site disorder
    'Springer Science and Business Media LLC', 2020
    Co-Authors: Bahadoran C., Mountford T., Ravishankar K., Saada E
    Abstract:

    We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. We prove quenched strong local equilibrium at subcritical and critical hydrodynamic densities, and dynamic local loss of mass at supercritical hydrodynamic densities. Our results do not assume starting from local Gibbs states. As byproducts of these results, we prove convergence of the process from given initial configurations with an asymptotic density of particles to the left of the origin. In particular, we relax the weak convexity assumption of Bahadoran et al. (Braz J Probab Stat 29(2):313-335, 2015; Ann Inst Henri Poincare Probab Stat 53(2):766-801, 2017) for the escape of mass property

  • Hydrodynamics In A Condensation Regime: The Disordered Asymmetric Zero-Range Process
    'Institute of Mathematical Statistics', 2020
    Co-Authors: Bahadoran C., Mountford T., Ravishankar K., Saada E
    Abstract:

    We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant

  • Hydrodynamics in a condensation regime: the disordered asymmetric zero-range process
    HAL CCSD, 2020
    Co-Authors: Bahadoran Christophe, Mountford T., Ravishankar K., Saada E
    Abstract:

    International audienceWe study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant

  • Hydrodynamics in a condensation regime: the disordered asymmetric zero-range process
    2019
    Co-Authors: Bahadoran Christophe, Mountford T., Ravishankar K., Saada E
    Abstract:

    We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded Nondecreasing Function of the number of particles. For any given environment satisfying suitable averaging properties, we establish a hydrodynamic limit given by a scalar conservation law including the domain above critical density, where the flux is shown to be constant.Comment: Annals of Probability, In pres