Hyperbolic Parabolic Limit, Maxwellian Iteration and Objectivity

2015 ◽  
pp. 353-361
Author(s):  
Tommaso Ruggeri ◽  
Masaru Sugiyama
Keyword(s):  
Parabolic Limit

PARABOLIC LIMIT AND STABILITY OF THE VLASOV–FOKKER–PLANCK SYSTEM

2000 ◽  
Vol 10 (07) ◽  
pp. 1027-1045 ◽  
Author(s):  
F. POUPAUD ◽  
J. SOLER
Keyword(s):  
Free Path ◽  
Space Dimension ◽  
Mass Density ◽  
Mean Free Path ◽  
Convergence Result ◽  
Limit Equation ◽  
Thermal Velocity ◽  
The Stability ◽  
Parabolic Limit ◽  
Fokker Planck

In this paper the stability of the Vlasov–Poisson–Fokker–Planck with respect to the variation of its constant parameters, the scaled thermal velocity and the scaled thermal mean free path, is analyzed. For the case in which the scaled thermal velocity is the inverse of the scaled thermal mean free path and the latter tends to zero, a parabolic limit equation is obtained for the mass density. Depending on the space dimension and on the hypothesis for the initial data, the convergence result in L1 is weak and global in time or strong and local in time.

scholarly journals Global existence of classical solutions for a hyperbolic chemotaxis model and its parabolic limit

2006 ◽  
Vol 55 (1) ◽  
pp. 289-316 ◽  
Author(s):  
Hyung Ju Hwang ◽  
Kyungkeun Kang ◽  
Angela Stevens
Keyword(s):  
Global Existence ◽  
Classical Solutions ◽  
Chemotaxis Model ◽  
Parabolic Limit

scholarly journals The occurence of interstellar meteoroids in the vicinity of the Earth

2008 ◽  
Vol 4 (S251) ◽  
pp. 347-348 ◽  
Author(s):  
Mária Hajduková
Keyword(s):  
Data Center ◽  
Hyperbolic Orbit ◽  
The Earth ◽  
Order Of Magnitude ◽  
Interstellar Material ◽  
Heliocentric Velocity ◽  
Parabolic Limit ◽  
Meteor Data ◽  
After Error

AbstractIf interstellar meteors are present among the registered meteor orbits, the distribution of the excesses of their heliocentric velocities should correspond to the distribution of radial velocities of close stars. Hence, for the velocity vi = 20 kms−1 of an interstellar meteor (with respect to the Sun) we obtain a heliocentric velocity vH = 46.6 kms−1 of an interstellar meteor arriving at the Earth. Moreover, a concentration of radiants to the Sun's apex should be observed. An analysis of the hyperbolic meteors among the 4581 photographic orbits of the IAU Meteor Data Center showed that the identification of the vast majority of the hyperbolic orbits in these catalogues has been caused by an erroneous determination of their heliocentric velocity and/or other parameters. Any error in the determination of vH, especially near the parabolic limit, can create an artificial hyperbolic orbit that does not really exist. On the basis of photographic meteors from the IAU MDC, the proportion of possible interstellar meteors decreased significantly (greater than 1 order of magnitude) after error analysis and does not exceed the value 2.5 × 10−4. Neither any concentration of radiants to the Sun's apex, nor any distribution following the motion of interstellar material has been found.

scholarly journals On a singularly perturbed wave equation with dynamic boundary conditions

2004 ◽  
Vol 134 (2) ◽  
pp. 389-413 ◽  
Author(s):  
Luminiţa Popescu ◽  
Aníbal Rodriguez-Bernal
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Limit Problem ◽  
Linear Wave ◽  
Dynamic Boundary Conditions ◽  
Boundary Damping ◽  
Perturbation Problem ◽  
Dynamic Boundary ◽  
Linear Wave Equations ◽  
Parabolic Limit

In this paper we analyse a singular perturbation problem for linear wave equations with interior and boundary damping. We show how the solutions converge to the formal parabolic limit problem with dynamic boundary conditions. Conditions are given for uniform convergence in the energy space.

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