Shock-Layer Bounds for a Singularly Perturbed Equation

Abstract

The size of the shock layer governed by a conservation laws is studied. The conservation law is a parabolic reaction-convection-diffusion equation with a small parameter multiplying the diffusion term and convex flux. Rigorous upper and lower bounding functions for the solution of the conservation law are established based on maximum principle arguments. The bounding functions demonstrate that the size of the shock layer is proportional to the parameter multiplying the diffusion term. Keywords: Asymptotics, Hyperbolic differential equations, Maximum principle.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1990
Accession Number
ADA227458

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  • Jeffrey S. Scroggs

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  • Boundaries
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Fields of Study

  • Mathematics

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  • Calculus or Mathematical Analysis
  • Fluid Dynamics.