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Factorization for non-symmetric operators and exponential H-theorem
We present an abstract method for deriving decay estimates on the resolvents and semigroups of non-symmetric operators in Banach spaces in terms of estimates in another smaller reference BanachExpand
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On the spatially homogeneous Boltzmann equation
Abstract We consider the question of existence and uniqueness of solutions to the spatially homogeneous Boltzmann equation. The main result is that to any initial data with finite mass and energy,Expand
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The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach.
Our starting point is a selection-mutation equation describing the adaptive dynamics of a quantitative trait under the influence of an ecological feedback loop. Based on the assumption of small (butExpand
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General relative entropy inequality: an illustration on growth models
Abstract We introduce the notion of General Relative Entropy Inequality for several linear PDEs. This concept extends to equations that are not conservation laws, the notion of relative entropy forExpand
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Stability, Convergence to Self-Similarity and Elastic Limit for the Boltzmann Equation for Inelastic Hard Spheres
We consider the spatially homogeneous Boltzmann equation for inelastic hard spheres, in the framework of so-called constant normal restitution coefficients$${\alpha \in [0,1]}$$ . In the physicalExpand
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On Kac's chaos and related problems
This paper is devoted to establish quantitative and qualitative estimates related to the notion of chaos as firstly formulated by M. Kac \cite{Kac1956} in his study of mean-field limit for systems ofExpand
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From the Becker–Döring to the Lifshitz–Slyozov–Wagner Equations
Connections between two classical models of phase transitions, the Becker–Döring (BD) equations and the Lifshitz–Slyozov–Wagner (LSW) equations, are investigated. Homogeneous coefficients areExpand
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On The Trace Problem For Solutions Of The Vlasov Equation
We study tlie trace problem for weak solutions of the Vlasov equation set in a domain. When the force field has Sobolev regularity, we prove the existence of a trace on the boundaries, which isExpand
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From the discrete to the continuous coagulation–fragmentation equations
The connection between the discrete and the continuous coagulation–fragmentation models is investigated. A weak stability principle relying on a priori estimates and weak compactness in L1 isExpand
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Global existence for the discrete diffusive coagulation-fragmentation equations in $L^1$
Existence of global weak solutions to the discrete coagulation-fragmentation equations with diffusion is proved under general assumptions on the coagulation and fragmentation coefficients. UnlikeExpand
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