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Zeroelectronmass limit of EulerPoisson equations, Discrete Contin
 Dyn. Syst. Ser. A
, 2013
"... ar ..."
THE ZEROELECTRONMASS LIMIT IN THE HYDRODYNAMIC MODEL FOR PLASMAS
"... Abstract. The limit of vanishing ratio of the electron mass to the ion mass in the isentropic transient EulerPoisson equations with periodic boundary conditions is proved. The equations consist of the conservation laws for the electron density and current density for given ion density, coupled to t ..."
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Cited by 5 (1 self)
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which needs to be controlled. This is done by a reformulation of the equations in terms of the enthalpy, higherorder energy estimates and a careful use of the Poisson equation. AMS Classification. 35B25, 35L60, 35L65, 35Q35, 82D10. Keywords. EulerPoisson system, limit of vanishing electron mass
QUANTUM EULERPOISSON SYSTEMS: EXISTENCE OF STATIONARY STATES
"... Abstract. A onedimensional quantum EulerPoisson system for semiconductors for the electron density and the electrostatic potential in bounded intervals is considered. The existence and uniqueness of strong solutions with positive electron density is shown for quite general (possibly nonconvex or ..."
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Abstract. A onedimensional quantum EulerPoisson system for semiconductors for the electron density and the electrostatic potential in bounded intervals is considered. The existence and uniqueness of strong solutions with positive electron density is shown for quite general (possibly non
QUASINEUTRAL LIMIT OF THE NONISENTROPIC EULERPOISSON SYSTEM
"... Abstract. This paper is concerned with multidimensional nonisentropic EulerPoisson equations for plasmas or semiconductors. By using the method of formal asymptotic expansions, we analyse the quasineutral limit for Cauchy problems with prepared initial data. It is shown that the small parameter pro ..."
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Cited by 3 (0 self)
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Abstract. This paper is concerned with multidimensional nonisentropic EulerPoisson equations for plasmas or semiconductors. By using the method of formal asymptotic expansions, we analyse the quasineutral limit for Cauchy problems with prepared initial data. It is shown that the small parameter
Critical Thresholds in EulerPoisson Equations
, 2001
"... We present a preliminary study of a new phenomena associated with the EulerPoisson equations  the so called critical threshold phenomena, where the answer to questions of global smoothness vs. finite time breakdown depends on whether the initial configuration crosses an intrinsic, O(1) critica ..."
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Cited by 53 (26 self)
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We present a preliminary study of a new phenomena associated with the EulerPoisson equations  the so called critical threshold phenomena, where the answer to questions of global smoothness vs. finite time breakdown depends on whether the initial configuration crosses an intrinsic, O(1
Travelling wave analysis of an isothermal EulerPoisson model.
, 1994
"... : We present a travelling wave analysis of the isothermal Euler equations for electrons and ions coupled by the Poisson equation. The analysis is based on a phase plane analysis which leads to three types of generic solutions. 1 Introduction. The Euler Poisson system is used to describe the dynami ..."
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Cited by 4 (0 self)
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the dynamics of a plasma consisting of electrons and ions in their self consistent electric field. In plasma physics, it is very often assumed that the plasma is quasineutral. The quasineutrality assumption can be viewed mathematically as a singular limit of the full EulerPoisson model which leads to a
Quasineutral limit of the EulerPoisson and EulerMongeAmpère systems
 Comm. Partial Differential Equations
, 2005
"... This paper studies the pressureless EulerPoisson system and its fully nonlinear counterpart, the EulerMongeAmpère system, where the fully nonlinear MongeAmpère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a geometr ..."
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Cited by 8 (2 self)
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This paper studies the pressureless EulerPoisson system and its fully nonlinear counterpart, the EulerMongeAmpère system, where the fully nonlinear MongeAmpère equation substitutes for the linear Poisson equation. While the first is a model of plasma physics, the second is derived as a
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
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