摘要:

We show the nonlinear stability of small bifurcating stationary rolls u , , for the Swift–Hohenberg–equation on the domain R2. In Bloch wave representation the linearization around a marginal stable roll uε,x, has continuous spectrum up to 0 with a locally parabolic shape at the critical Bloch vector 0. Using an abstract renormalization theorem we show that small spatially localized integrable perturbations decay diffusively to zero. Moreover we estimate the size of the domain of attraction of a roll uε,x, in terms of its modulus and Fourier wavenumber. To explain the method we also treat the nonlinear stability of stationary rolls for the complex Swift–Hohenberg equation on R2

ISSN:0360-5302    

DOI:10.1080/03605309908821496

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309908821497

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

We introduce for the system of pressureless gases a new notion of solution, which consist in interpreting the system as two nonlinearly coupled linear equations. We prove In this setting existence of solutions for the Cauchy Problem, as well as uniqueness under optimal conditions on initlaffata. The proofs rely on the detailed study of the relations between pressureless gases, tie dynamics of sticky particles and nonlinear scalar conservation laws with monotone initial data. We prove for the latter problem that monotonicit implies uniqueness. and a generalization of Oleinik's entropy condition

ISSN:0360-5302    

DOI:10.1080/03605309908821498

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309908821499

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309908821500

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

摘要:

We give a new derivation of the minimal velocity estimates [27] for unitary evolutions with some optimal estimates. Let H and A be selfadjoint operators on a Hilbert space H. The starting point is Mourre's inequalitywhich is supposed to hold in form sense on the spectral subspaceof H for some interval. The second assumption is that the multiple commutatorsare well-behaved forThen we show that, for a dense set ofinand allmis contained in the spectral subspaceup to an error of order t-min norm. We apply this general result to the case where H is a Schrödinger operator on Rnand A the dilation generator, proving thatis asymptotically supported in the setup to an error of order t-min norm.

ISSN:0360-5302    

DOI:10.1080/03605309908821502

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor

ISSN:0360-5302    

DOI:10.1080/03605309908821488

出版商:Marcel Dekker, Inc.    

年代:1999

数据来源: Taylor