摘要:

T. Global in time solutions of the equations Ou = H(u, u') on Minkowski space-time are considered. Results available so far involve complicated decay and energy estimates and also careful choice of Banach spaces and associated ordinary differential inequalities. This work tries to simplify some of the existing arguments and to develop a new technique for other nonlinear evolution equations. The method is motivated by the work of Christodoulou and Baez, Segal, and Zhou, on nonlinear wave equations. The key idea is to use the Penrose conformal compactification that transforms the equations from Minkowski space to the Einstein universe in order to change the global existence question to the local one.

ISSN:0360-5302    

DOI:10.1080/03605309908821503

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309908821501

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

In this paper a biharmonic problem with Navier boundary condition involving nearly critical growth is considered: △2=u(n+4)/(n-4)-ru > 0 inΩ and u=△u=0 on ∂Ω, where iΩs a bounded smooth convex domain in Rn(n≥5) and r > 0 is small. We show that any sequence of positive solutions with r→0 has to blow up and concentrate at finitely many points in the interior of the domain ω. With blow-up argument, we also give the energy a priori estimate of positive solutions.

ISSN:0360-5302    

DOI:10.1080/03605309908821504

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

We investigate a phenomeno of boundary layer formation which occurs for large times near the free boundary of monnegative solutions to the nonlinear heat-conduction equation with absorption

ISSN:0360-5302    

DOI:10.1080/03605309908821489

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309908821490

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

We consider the one-dimensional equations of an isentropic gas with γ= 3. We show in this article that every bounded measurable entropy-admissible solution lies inTo do so, we use thc kinetic formulation due to Lions, Perthame and Tadmor.

ISSN:0360-5302    

DOI:10.1080/03605309908821491

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

We invcestigat, the existcnce and uniqueness of non-negative weak solutions towith initial data in the spacc of bounded and non-negative measures whenand inwhcnprovided that q is large enougli. Non-cxistc.ncc of solutions with Dirac masses as initial data is also shown whenWe finally study the large time behaviour of the L1-nor111 of t,he solutions to the Cauchy problem, thereby extending previous results to ii wider class of initial data. One main step in our approach is the derivation of drcay estimates of theL∞-norm of the gradient of

ISSN:0360-5302    

DOI:10.1080/03605309908821492

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

The purpose of this paper is to extend known existence results for Hamilton-Jacobi-Bellman equations. The classical results give existence, uniqueness and Holder regularity when all elliptic operators involved have nonpositive zero-order term. We want to handle here the more general case where they have principal eigenvalues bounded below by a positive constant. As a motivation for this work, we give an application to the study of the Maximum Principle in infinite cylinders, following a work by Berestycki, Caffarelli and Nirenberg [2]. This is used to extend the cylindrical symmetry result in [2] to a more general class of operators.

ISSN:0360-5302    

DOI:10.1080/03605309908821493

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309908821494

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

A n-dimensional quasiliner wave equation with nonlinear boundary dissipation is considered. Global existence, uniqueness and uniform decay rates are established for the model, under the assumption that the H1(Ω)xL2(Ω') norms of the initial data are sufficiently small. The result presented in this paper extends/generalizes those obtained those obtained recently in (13), where, by contrast, interior nonlinear damping was considered; and those obtained in (31), where the one-dimensional wave equation with linear boundary damping was treated.

ISSN:0360-5302    

DOI:10.1080/03605309908821495

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor