摘要:

In this paper, we consider the Euler equations with spherical symmetry inoutside a region of the center. By assuming an outing absorbing boundary and within the leading term with respect to the amplitude of wave strength, we prove that there exists a uniform bound for the approximate solutions constructed by Glimm's scheme. This implies that the main difficulty left for the full nonlinear system whenx≥1 is to estimate the infinite reflections of waves inside the region, whereis the supremum of the absolute value of the characteristics under consideration.

ISSN:0360-5302    

DOI:10.1080/03605309908821416

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

We calculate the number of bound states appearing below the spectrum of a semi—bounded operator in the case of a weak, indefinite perturbation. The abstract result generalizes the Birman—Schwinger principle to this case. We discuss a number of examples, in particular higher order differential operators, critical Schrodinger operators, systems of second order differential operators, Schrodinger type operators with magnetic fields and the Two—dimensional Pauli operator with a localized magnetic field.

ISSN:0360-5302    

DOI:10.1080/03605309908821417

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309908821418

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

A general stability and convergence theorem is established for generalized solutions of a family of nonlinear evolution equations with non-local diffusion in one space dimension. As the first application we justify the motion by crystalline energy as a limit of regularized problems. As the sec-ond application we show the convergence of crystalline algorithm for general curvature flow equations. Our general results are also important to explain that geometric evolution of crystals depends continuously on temperature even if facets appear.

ISSN:0360-5302    

DOI:10.1080/03605309908821419

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309908821420

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

Abstract. This paper studies the asymptotic behavior of the solutions of massive coupled Maxwell—Klein—Gordon field equations in the 4—dimensional Minkowski space for the case of small initial data with charge. The proof relies on gauge invariant energy estimates and geometric properties of the fields equations. The presence of charge together with the mass term in the Klein—Gordon equation are the novelties of this project and provide us with a situation which cannot be accomodated by standard methods such as the conformal transformation. A covariant Lie derivative operator for the Klein—Gordon field is introduced and allows us to handle the most troublesome terms in the error estimates.

ISSN:0360-5302    

DOI:10.1080/03605309908821421

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

Abstract. In this paper I derive a gauge invariant decay estimate of the solutions of massive Maxwell—Klein—Gordon fields equations in the 4—dimensional Minkowski space, provided that the initial energy of the system is bounded. This estimate implies that the Klein—Gordon field decays to zero in the local L2norm. I also show that the local energy decays. The proof is based on gauge invariant energy identities.

ISSN:0360-5302    

DOI:10.1080/03605309908821422

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

We consider several selfadjointh-pseudodifferential operatorswhich commute to each other. Letbe a regular value of the principal symbolofA(h) andKbe a compact neighborhood ofE. Under suitable assumptions the joint spectrum ofA(h) inKconsists of finitely many joint eigenvalues. Let ζ be a smooth function in Rkhaving a Fourier transform with compact support. The aim of this article is to investigate the semiclassical asymptotics of the tracein terms of the periodic orbits of the joint Hamiltoian flow of a0lying on the energy surface.

ISSN:0360-5302    

DOI:10.1080/03605309908821423

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309908821424

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309908821425

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor