On Singular Semilinear Elliptic Equations

Abstract

We study the singular semilinear elliptic equation. This type of equation arises in the boundary layer theory of viscous fluids. From the results it follows that the equation has a unique classical solution within a bounded domain omega, where p(x) is a sufficiently regular function which is positive on omega. Kusano and Swanson gave the existence proof on exterior domains. In this paper we show via the upper and lower solution method, which is also referred to as the barrier method, that the equation has a bounded positive entire solution vanishing at infinity. It is observed by Callegari, Friedman and Nachman that if the partial differential equations describing the boundary layer behind a rarefaction or shock wave (with viscosity proportional to the temperature) traveling down, and perpendicular to, a flat plate are written in terms of a stream function and a similarity variable the following Blasius-type equation emerges.

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Document Details

Document Type
Technical Report
Publication Date
May 08, 1991
Accession Number
ADA238784

Entities

People

  • Aihua W. Shaker

Organizations

  • Naval Postgraduate School

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Communities of Interest

  • C4I

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  • Abstracts
  • Boundaries
  • Boundary Layer
  • Boundary Value Problems
  • California
  • Differential Equations
  • Electrical Engineering
  • Engineering
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  • Mathematics
  • New York
  • Partial Differential Equations
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Fields of Study

  • Mathematics

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  • Analytical Mechanics
  • Calculus or Mathematical Analysis
  • Combustion Dynamics and Shock Wave Physics.