SOLUTION OF A NON-LINEAR BOUNDARY VALUE PROBLEM IN FLUID MECHANICS USING A VARIATIONAL METHOD,

Abstract

It is shown that the generalized Dirichlet integral has similar variational properties as the ordinary one, i.e. the solution of the corresponding first boundary value problem makes it minimum for given boundary values. It is shown that the compound variational functional introduced has a lower bound for a broad function class, ('admissible' functions) thus permitting the formulation of the variational problem as a minimum problem. A non-linear integral equation is derived involving only the boundary values of Q. This integral equation is essentially equivalent to the boundary value problem. With the aid of this integral equation the asymptotic estimates near 0 are improved and differentiability properties of Q on the boundary are proved.

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1965
Accession Number
AD0629629

Entities

People

  • Alexander Pal

Organizations

  • New York University Tandon School of Engineering

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Computational Science
  • Dirichlet Integral
  • Equations
  • Fluid Dynamics
  • Fluid Mechanics
  • Integral Equations
  • Integrals
  • Mechanics
  • Variational Methods

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis