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On selfsimilarity and stationary problem for fragmentation and coagulation
"... We prove the existence of a stationary solution of any given mass to the coagulationfragmentation equation without assuming a detailed balance condition, but assuming instead that aggregation dominates fragmentation for small particles whisle fragmentation predominates for large particles. We also s ..."
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Cited by 22 (8 self)
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We prove the existence of a stationary solution of any given mass to the coagulationfragmentation equation without assuming a detailed balance condition, but assuming instead that aggregation dominates fragmentation for small particles whisle fragmentation predominates for large particles. We also show the existence of a self similar solution of any given mass to the coagulation equation and to the fragmentation equation for kernels satisfying a scaling property. These results are obtained by applying a simple abstract result of functional analysis based on the Tykhonov fixed point theorem, and which slightly generalizes a method introduced in [26]. Moreover, we show that the solutions to the fragmentation equation with initial data of a given mass behaves, as t → +∞, as the self similar solution of the same mass. 1 Introduction and
The Theory Of Generalized Dirichlet Forms And Its Applications In Analysis And Stochastics
, 1996
"... We present an introduction (also for nonexperts) to a new framework for the analysis of (up to) second order differential operators (with merely measurable coefficients and in possibly infinitely many variables) on L²spaces via associated bilinear forms. This new framework, in particular, covers b ..."
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Cited by 18 (1 self)
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We present an introduction (also for nonexperts) to a new framework for the analysis of (up to) second order differential operators (with merely measurable coefficients and in possibly infinitely many variables) on L²spaces via associated bilinear forms. This new framework, in particular, covers both the elliptic and the parabolic case within one approach. To this end we introduce a new class of bilinear forms, socalled generalized Dirichlet forms, which are in general neither symmetric nor coercive, but still generate associated C0 semigroups. Particular examples of generalized Dirichlet forms are symmetric and coercive Dirichlet forms (cf. [FOT], [MR1]) as well as time dependent Dirichlet forms (cf. [O1]). We discuss many applications to differential operators that can be treated within the new framework only, e.g. parabolic differential operators with unbounded drifts satisfying no L p conditions, singular and fractional diffusion operators. Subsequently, we analyz...
Sensitivity Analysis For Atmospheric Chemistry Models Via Automatic Differentiation
 Environ
, 1997
"... . Automatic differentiation techniques are used in the sensitivity analysis of a comprehensive atmospheric chemical mechanism. Specifically, ADIFOR software is used to calculate the sensitivity of ozone with respect to all initial concentrations (of 84 species) and all reaction rate constants (178 c ..."
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Cited by 13 (4 self)
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. Automatic differentiation techniques are used in the sensitivity analysis of a comprehensive atmospheric chemical mechanism. Specifically, ADIFOR software is used to calculate the sensitivity of ozone with respect to all initial concentrations (of 84 species) and all reaction rate constants (178 chemical reactions) for six different chemical regions. Numerical aspects of the application of ADIFOR are also presented. Automatic differentiation is shown to be a powerful tool for sensitivity analysis. Key words. Atmospheric chemistry, Automatic Differentiation. 1. Introduction. Comprehensive sensitivity analysis of air pollution models remains the exception rather than the rule. Most sensitivity analysis applied to air pollution modeling studies has focused on the calculation of the local sensitivities (first order derivatives of output variables with respect to model parameters) in box model studies of gas phase chemistry (see [Cho86]). The most common form of sensitivity studies with ...
Meagre Functions and Asymptotic Behaviour of Dynamical Systems
 METHODS & APPLICATIONS
, 2001
"... A measurable function x : J ae R! X (X a metric space) is said to be Cmeagre if C ae X is nonempty and, for every closed set K ae X with K " C = ;, x \Gamma1 (K) has finite Lebesgue measure. This concept of meagreness is shown to provide a unifying framework which facilitates a variety of ch ..."
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Cited by 6 (5 self)
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A measurable function x : J ae R! X (X a metric space) is said to be Cmeagre if C ae X is nonempty and, for every closed set K ae X with K " C = ;, x \Gamma1 (K) has finite Lebesgue measure. This concept of meagreness is shown to provide a unifying framework which facilitates a variety of characterizations, extensions or generalizations of diverse facts pertaining to asymptotic behaviour of dynamical systems.
Singular perturbations of finite dimensional gradient flows. Discrete
 A
"... Abstract. In this paper we give a description of the asymptotic behavior, as ε → 0, of the εgradient flow in the finite dimensional case. Under very general assumptions we prove that it converges to an evolution obtained by connecting some smooth branches of solutions to the equilibrium equation (s ..."
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Cited by 4 (0 self)
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Abstract. In this paper we give a description of the asymptotic behavior, as ε → 0, of the εgradient flow in the finite dimensional case. Under very general assumptions we prove that it converges to an evolution obtained by connecting some smooth branches of solutions to the equilibrium equation (slow dynamics) through some heteroclinic solutions of the gradient flow (fast dynamics). 1.
The Current State And The Future Directions In Air Quality Modeling
 MODELLING AND SIMULATION OF COMPLEX ENVIRONMENTAL PROBLEMS
, 1996
"... In this paper the present "state" of air quality modeling (as viewed by the authors) is presented. The focus of the paper will be on the "current" stateofaffairs. Due to limitation of space (and the focus of this Dagstuhl Seminar) the discussion will focus on only a few aspects of air quality mode ..."
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Cited by 3 (2 self)
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In this paper the present "state" of air quality modeling (as viewed by the authors) is presented. The focus of the paper will be on the "current" stateofaffairs. Due to limitation of space (and the focus of this Dagstuhl Seminar) the discussion will focus on only a few aspects of air quality modeling: i.e., chemical integration, sensitivity analisys and computational framework.
AN EXTENSION THEOREM IN SYMPLECTIC GEOMETRY
, 2001
"... Abstract. We extend the “Extension after Restriction Principle” for symplectic embeddings of bounded starlike domains to a large class of symplectic embeddings of unbounded starlike domains. 1. ..."
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Cited by 2 (0 self)
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Abstract. We extend the “Extension after Restriction Principle” for symplectic embeddings of bounded starlike domains to a large class of symplectic embeddings of unbounded starlike domains. 1.
SEMIGROUPS FOR GENERAL TRANSPORT EQUATIONS WITH ABSTRACT BOUNDARY CONDITIONS
, 2006
"... ABSTRACT. We investigate C0semigroup generation properties of the Vlasov equation with general boundary conditions modeled by an abstract boundary operator H. For multiplicative boundary conditions we adapt techniques from [14] and in the case of conservative boundary conditions we show that there ..."
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Cited by 2 (1 self)
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ABSTRACT. We investigate C0semigroup generation properties of the Vlasov equation with general boundary conditions modeled by an abstract boundary operator H. For multiplicative boundary conditions we adapt techniques from [14] and in the case of conservative boundary conditions we show that there is an extension A of the free streaming operator TH which generates a C0semigroup (VH(t))t�0 in L 1. Furthermore, following the ideas of [4], we precisely describe its domain and provide necessary and sufficient conditions ensuring that (VH(t))t�0 is stochastic. Let us consider the general transport equation 1.
Rightinvariant Sobolev metrics of fractional order on the diffeomorphism group of the circle. arXiv:1202.5122v2
, 2012
"... Abstract. In this paper we study the geodesic flow of a rightinvariant metric induced by a general Fourier multiplier on the diffeomorphisms group of the circle and on some of its homogeneous spaces. This study covers in particular rightinvariant metrics induced by Sobolev norms of fractional orde ..."
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Cited by 2 (0 self)
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Abstract. In this paper we study the geodesic flow of a rightinvariant metric induced by a general Fourier multiplier on the diffeomorphisms group of the circle and on some of its homogeneous spaces. This study covers in particular rightinvariant metrics induced by Sobolev norms of fractional order. We show that, under a certain condition on the symbol of the inertia operator (which is satisfied for the fractional Sobolev norm H s for s ≥ 1/2), the corresponding initial value problem is wellposed in the smooth category and that the Riemannian exponential map is a smooth local diffeomorphism. Paradigmatic examples of our general setting cover, besides all traditional Euler equations induced by a local inertia operator, the ConstantinLaxMajda equation, and the EulerWeilPetersson equation.