摘要:

AbstractWe study the partial differential equationwhich arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × RS1. We establish existence, uniqueness, and regularity of solutions, locally in time, for positive initial data inH1(S1), and prove the existence of several families of Lyapunov functions for the evolution. From the latter we establish a sharp connection between existence globally in time and positivity preservation: if [0],T*) is a maximal half open interval of existence for a positive solution of the equation, withT*(1 + √3)/16π2√3 thenT* = ∞ and limt∞ w(t,.)exists and is constant. We discuss also some explicit solutions and propose a generalization to higher dimensions. © 1994 John Wi

ISSN:0010-3640    

DOI:10.1002/cpa.3160470702

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.3160470703

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

年代:1994

数据来源: WILEY

摘要:

AbstractA link is found between quasiconvexity and the conditions for a setLof conductivity or elasticity tensors to be stable under lamination. These conditions, derived in the companion paper, are shown here to be equivalent to the condition that for every pointBon the boundary of the setLan operatorTBdependent on the tangent plane and curvature of the set atBis a quasiconvex translation operator. A separate class of quasiconvex translation operators is obtained which are candidates for proving thatLis stable under homogenization. The region stable under homogenization associated with any one of these operators shares a common boundary point and tangent plane with the setLand has curvature at that point not greater than the curvature ofL.The conditions under which there exists a representative subclass of these operators such that the associated regions stable under homogenization wrap aroundLremains unresolved. It is proved thatLcan be characterized by minimizations of sums and dual energies in much the same way that convex sets can be characterized by their Legendre transforms. © 1994 John Wiley&Sons, Inc

ISSN:0010-3640    

DOI:10.1002/cpa.3160470704

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.3160470705

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.3160470701

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

年代:1994

数据来源: WILEY