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47
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 29 (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...
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 25 (9 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
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 17 (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 ...
A Semilinear Fourth Order Elliptic Problem with Exponential Nonlinearity
, 2003
"... We study a semilinear fourth order elliptic problem with exponential nonlinearity. Motivated by a question raised in [Li], we partially extend known results for the corresponding second order problem. Several new difficulties arise and many problems still remain to be solved. We list the ones we fee ..."
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Cited by 12 (2 self)
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We study a semilinear fourth order elliptic problem with exponential nonlinearity. Motivated by a question raised in [Li], we partially extend known results for the corresponding second order problem. Several new difficulties arise and many problems still remain to be solved. We list the ones we feel particularly interesting in the final section. Mathematics Subject Classification: 35J65; 35J40. 1
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 ..."
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Cited by 8 (7 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.
Asymptotic behaviour of nonlinear systems
 The American Mathematical Monthly
, 2004
"... processes are of great importance in the applications of differential equations, dynam ..."
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Cited by 6 (1 self)
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processes are of great importance in the applications of differential equations, dynam
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 ..."
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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.
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.