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Nonlinear Evolution Equations That Change Type pp 32–46Cite as

Composite Type, Change of Type, and Degeneracy in First Order Systems with Applications to Viscoelastic Flows

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Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 27))

Abstract

In this paper we discuss some features of systems of partial differential equations of first order related to change of type, to composite type and to degeneracy. 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.

This work was supported by the National Science Foundation under grant # DMS-8714152.

Work supported by ARO grant # DAAL03–88-K-0132

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    L. Pamela Cook, G. Schleiniger & R. J. Weinacht

Authors
  1. L. Pamela Cook
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  2. G. Schleiniger
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  3. R. J. Weinacht
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Houston, Houston, Texas, 77204, USA

    Barbara Lee Keyfitz

  2. Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 27695, USA

    Michael Shearer

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© 1990 Springer-Verlag New York Inc.

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Cook, L.P., Schleiniger, G., Weinacht, R.J. (1990). Composite Type, Change of Type, and Degeneracy in First Order Systems with Applications to Viscoelastic Flows. In: Keyfitz, B.L., Shearer, M. (eds) Nonlinear Evolution Equations That Change Type. The IMA Volumes in Mathematics and Its Applications, vol 27. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9049-7_3

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  • DOI: https://doi.org/10.1007/978-1-4613-9049-7_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9051-0

  • Online ISBN: 978-1-4613-9049-7

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