ISSN:0010-3640    

DOI:10.1002/cpa.3160471002

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractThe solution of the KdV equation with single‐minimum initial data has a zero‐dispersion limit characterized by Lax and Levermore as the solution of an infinite‐dimensional constrained quadratic minimization problem. An adaptive numerical method for computing the weak limit from this characterization is constructed and validated. The method is then used to study the weak limit. Initial simple experiments confirm theoretical predictions, while experiments with more complicated data display multiphase behavior considerably beyond the scope of current theoretical analyses. The method computes accurate weak limits with multiphase structures sufficiently complex to provide useful test cases for the calibration of numerical averaging algorithms. © 1994 John Wiley&Son

ISSN:0010-3640    

DOI:10.1002/cpa.3160471003

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

摘要:

AbstractWe consider Cauchy problems for the 1‐D one component Vlasov‐Poisson and Fokker‐Planck‐Poisson equations with the initial electron density being in the natural space of arbitrary non‐negative finite measures. In particular, the initial density can be a Dirac measure concentrated on a curve, which we refer to as “electron sheet” initial data. These problems resemble both structurally and functional analytically Cauchy problems for the 2‐D Euler and Navier‐Stokes equations (in vorticity formulation) with vortex sheet initial data. Here, we need to define weak solutions more specifically than usual since the product of a finite measure with a function of bounded variation is involved. We give a natural definition of the product, establish its weak stability, and existence of weak solutions follows. Our concept of weak solutions through the newly defined product is justified since solutions to the Fokker‐Planck‐Poisson equation, the analogue of Navier‐Stokes equation, are shown to converge to weak solutions of the Vlasov‐Poisson equation as the Fokker‐Planck term vanishes. The main difficulty is the aforementioned weak stability which we establish through a careful analysis of the explicit structure of these equations. This is needed because the problem studied here is beyond the range of applicability of the “velocity averaging” compactness methods of DiPerna‐L

ISSN:0010-3640    

DOI:10.1002/cpa.3160471004

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160471005

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160471001

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1994

数据来源: WILEY