Steady State of a Non-Linear Evolutionary Equation,

Abstract

Steady states of a class of nonlinear evolutionary equations with inhomogeneous (source) terms are investigated. First, the question of when the initial value problems corresponding to the evolutionary equations possess a steady state is discussed. Then, for a wide class of cases, we show that the steady state of the inhomogeneous problem is the same as the steady state of another problem without sources, but with different initial data. A direct proof of this result is given for the one-phase Stefan problem. In this case we also analyze the extent to which the conditions under which the general theorem is proved can be relaxed. An application shows that a free boundary problem in anodic smoothing is equivalent to a steady state one-phase Stefan problem. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 09, 1978
Accession Number
ADA064113

Entities

People

  • Joel C. W. Rogers

Organizations

  • Johns Hopkins University

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Boundaries
  • Convergence
  • Diffusion
  • Equations
  • Machining
  • Military Research
  • Physics
  • Physics Laboratories
  • Security
  • Steady State
  • Two Dimensional
  • Water Waves

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Government and Public Administration Law.