Singularly Perturbed Hyperbolic Evolution Problems with Infinite Delay and an Application to Polymer Rheology.

Abstract

We prove an existence theorem locally in time for quasilinear hyperbolic equations, in which the coefficients are allowed to depend on the history of the dependent variable. Singular perturbations, which change the type of the equation to parabolic, are included, and continuous dependence of the solutions on the perturbation parameter is shown. It is demonstrated that, for a substantial number of constitutive models suggested in the literature, the stretching of filaments of polymeric liquids is described by equations of the kind under study here. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1982
Accession Number
ADA116212

Entities

People

  • Michael Renardy

Organizations

  • University of Wisconsin–Madison

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  • Autonomy
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  • Boundary Value Problems
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Fields of Study

  • Mathematics

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  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
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