By A. V. Azevedo, D. Marchesin (auth.), Barbara Lee Keyfitz, Michael Shearer (eds.)
This IMA quantity in arithmetic and its functions NONLINEAR EVOLUTION EQUATIONS that modify variety is predicated at the court cases of a workshop which used to be a vital part of the 1988-89 IMA application on NONLINEAR WAVES. The workshop focussed on prob lems of ill-posedness and alter of kind which come up in modeling flows in porous fabrics, viscoelastic fluids and solids and part adjustments. We thank the Coordinat ing Committee: James Glimm, Daniel Joseph, Barbara Lee Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for making plans and enforcing a thrilling and stimulating year-long application. We specially thank the workshop organizers, Barbara Lee Keyfitz and Michael Shearer, for his or her efforts in bringing jointly a number of the significant figures in these examine fields within which theories for nonlinear evolution equations that adjust style are being constructed. A vner Friedman Willard Miller, J r. ix PREFACE through the iciness and spring quarters of the 1988/89 IMA software on Non linear Waves, the difficulty of swap of sort in nonlinear partial differential equations seemed often. dialogue started with the January 1989 workshop on part Waves in Fluidized Beds, Sedimentation and Granular circulation; many of the papers within the complaints of that workshop current ideas designed to prevent the looks of swap of style in types for multiphase fluid flow.
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We are interested in these effects with respect to viscoelastic fluid flow and hence we focus on the properties of two particular models of differential type, the Upper Convected Maxwell model and the Bird-DeAguiar model. Friedrichs' theory of symmetric positive operators is discussed as a means for treating these indefinite type systems and its use is illustrated for two simple systems, one of composite type and one of degenerate elliptic type. Key words. viscoelastic flow, steady flow, composite systems, mixed-type systems, degenerate systems AMS(MOS) subject classifications.
Nonlinear Evolution Equations That Change Type by A. V. Azevedo, D. Marchesin (auth.), Barbara Lee Keyfitz, Michael Shearer (eds.)