ISSN:0010-3640    

DOI:10.1002/cpa.3160430102

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

年代:1990

数据来源: WILEY

摘要:

AbstractWe consider a class of singular Sturm‐Liouville problems with a nonlinear convection and a strongly coupling source. Our investigation is motivated by, and then applied to, the study of transonic gas flow through a nozzle. We are interested in such solution properties as the exact number of solutions, the location and shape of boundary and interior layers, and nonlinear stability and instability of solutions when regarded as stationary solutions of the corresponding convective reaction‐diffusion equations. Novel elements in our theory include a priori estimate for qualitative behavior of general solutions, a new class of boundary layers for expansion waves, and a local uniqueness analysis for transonic solutions with interior and boundary lay

ISSN:0010-3640    

DOI:10.1002/cpa.3160430103

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

年代:1990

数据来源: WILEY

摘要:

AbstractA general algebraic framework is developed for characterizing the set of possible effective tensors of composites. A transformation to the polarization‐problem simplifies the derivation of the Hashin‐Shtrikman variational principles and simplifies the calculation of the effective tensors of laminate materials. A general connection is established between two methods for bounding effective tensors of composites. The first method is based on the variational principles of Hashin and Shtrikman. The second method, due to Tartar, Murat, Lurie, and Cherkaev, uses translation operators or, equivalently, quadratic quasiconvex functions. A correspondence is established between these translation operators and bounding operators on the relevant non‐local projection operator, T1. An important class of bounds, namely trace bounds on the effective tensors of two‐component media, are given a geometrical interpretation: after a suitable fractional linear transformation of the tensor space each bound corresponds to a tangent plane to the set of possible tensors. A wide class of translation operators that generate these bounds is found. The extremal translation operators in this class incorporate projections onto spaces of antisymmetric tensors. These extremal translations generate attainable trace bounds even when the tensors of the two‐components are not well ordered. In particular, they generate the bounds of Walpole on the effective bulk modulus. The variational principles of Gibiansky and Cherkaev for bounding complex effective tensors are reviewed and used to derive some rigorous bounds that generalize the bounds conjectured by Golden and Papanicolaou. An isomorphism is shown to underlie their variational principles. This isomorphism is used to obtain Dirichlet‐type variational principles and bounds for the effective tensors of general non‐selfadjoint problems. It is anticipated that these variational principles, which stem from the work of Gibiansky and Cherkaev, will have applications in many fiel

ISSN:0010-3640    

DOI:10.1002/cpa.3160430104

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

年代:1990

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160430105

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

年代:1990

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160430101

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

年代:1990

数据来源: WILEY