Initial Value Problems for Viscoelastic Liquids.

Abstract

Cauchy problems for equations modelling non-Newtonian fluids are discussed and recent existence theorems for classical solutions, based on semigroup methods, are presented. Such existence results depend in a crucial manner on the symbol of the leading differential operator. Both parabolic and hyperbolic cases are discussed. In general, however, the leading differential operator may be of non-integral order, arising from convolution with a singular kernel. This has interesting implications concerning the propagation of singularities. In particular, there are cases where C infinity-smoothing coexists with finite wave speeds. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1983
Accession Number
ADA136425

Entities

People

  • Michael Renardy

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Banach Space
  • Boundary Value Problems
  • Cauchy Problem
  • Convolution
  • Differential Equations
  • Elastic Properties
  • Equations
  • Formulas (Mathematics)
  • Integrals
  • Materials
  • Mathematics
  • Navier Stokes Equations
  • Partial Differential Equations
  • Theorems
  • Three Dimensional
  • United States
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis