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| 1. |
Metastable patterns in solutions ofut= ϵ2uxx−f(u) |
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Communications on Pure and Applied Mathematics,
Volume 42,
Issue 5,
1989,
Page 523-576
J. Carr,
R. L. Pego,
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摘要:
AbstractWe consider the equation in question on the interval 0 ≦x≦ 1 having Neumann boundary conditions, withf(u)=F(u), whereFis a double well energy density with equal minima atu= ±1. The only stable states of the system are patternless constant solutions. But given two‐phase initial data, a pattern of interfacial layers typically forms far out of equilibrium. The ensuing nonlinear relaxation process is extremely slow: patterns persist for exponentially long times proportional to exp{A±l/ϵ, whereA ±2=F(±1) andlis the minimum distance between layers. Physically, a tiny potential jump across a layer drives its motion.We prove the existence and persistence of these metastable patterns, and characterise accurately the equations governing their motion. The point of view is reminiscent of center manifold theory: a manifold parametrising slowly evolving states is introduced, a neighbourhood is shown to be normally attracting, and the parallel flow is characterised to high relative accuracy. Proofs involve a detailed study of the Dirichlet problem, spectral gap analysis, and ener
ISSN:0010-3640
DOI:10.1002/cpa.3160420502
出版商:Wiley Subscription Services, Inc., A Wiley Company
年代:1989
数据来源: WILEY
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| 2. |
Optimal approximations by piecewise smooth functions and associated variational problems |
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Communications on Pure and Applied Mathematics,
Volume 42,
Issue 5,
1989,
Page 577-685
David Mumford,
Jayant Shah,
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ISSN:0010-3640
DOI:10.1002/cpa.3160420503
出版商:Wiley Subscription Services, Inc., A Wiley Company
年代:1989
数据来源: WILEY
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| 3. |
Geometry of KDV (5): Scattering from the Grassmannian viewpoint |
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Communications on Pure and Applied Mathematics,
Volume 42,
Issue 5,
1989,
Page 687-701
H. P. McKean,
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PDF (484KB)
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ISSN:0010-3640
DOI:10.1002/cpa.3160420504
出版商:Wiley Subscription Services, Inc., A Wiley Company
年代:1989
数据来源: WILEY
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| 4. |
A note on our previous paper: On the existence of Hermitian Yang–Mills connections in stable vector bundles |
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Communications on Pure and Applied Mathematics,
Volume 42,
Issue 5,
1989,
Page 703-707
K. Uhlenbeck,
S. T. Yau,
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ISSN:0010-3640
DOI:10.1002/cpa.3160420505
出版商:Wiley Subscription Services, Inc., A Wiley Company
年代:1989
数据来源: WILEY
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| 5. |
Erratum |
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Communications on Pure and Applied Mathematics,
Volume 42,
Issue 5,
1989,
Page 709-709
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PDF (21KB)
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ISSN:0010-3640
DOI:10.1002/cpa.3160420506
出版商:Wiley Subscription Services, Inc., A Wiley Company
年代:1989
数据来源: WILEY
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| 6. |
Forthcoming articles |
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Communications on Pure and Applied Mathematics,
Volume 42,
Issue 5,
1989,
Page -
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PDF (34KB)
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ISSN:0010-3640
DOI:10.1002/cpa.3160420507
出版商:Wiley Subscription Services, Inc., A Wiley Company
年代:1989
数据来源: WILEY
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