Asymptotic Analysis of Non-Linear Elliptic and Parabolic Singular Perturbations.

Abstract

Some classes of Non-linear Second Order Elliptic and Parabolic Partial Differential Operators affected by the presence of a small parameter epsilon are investigated. The reduced problem (epsilon = 0) is characterized by the appearence of a free boundary of the solutions. The Existence, Uniqueness and regularity results are established for both perturbed and reduced problems. Sharp two-sided estimates for the difference of the solutions of the perturbed and reduced problems are proved and some constructive procedures are found out for localizing and computing the free boundary of the reduced problem. The Kinetic Theory of membranes with enzymotic activity is one of the possible fields of applications of the results established, the small parameter being the so-called Michaelis' coefficient. Additional keywords: Netherlands; asymptotics; calculus of variations; convergence; Cauchy problem. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1985
Accession Number
ADA159705

Entities

People

  • L. S. Frank

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • Calculus
  • Cauchy Problem
  • Coefficients
  • Convergence
  • Differential Equations
  • Eigenvalues
  • Equations
  • Inequalities
  • Kinetic Theory
  • Mathematical Models
  • Membranes
  • Perturbations
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Molecular and Cellular Biochemistry
  • Statistical inference.