Numerical Solution of Ill Posed Problems in Partial Differential Equations.

Abstract

This project is concerned with several questions concerning the existence, uniqueness continuous data dependence and numerical computation of solutions of various ill posed problems in partial differential equations. Several problems involving reaction diffusion equations with and without convection terms present were studied. In the latter case the ability of finite element approximate solutions to reproduce the continuous time dynamics was investigated. In the former case a convective diffusion equation with a similar source in the boundary condition was analyzed. A fairly complete picture of the dynamics was obtained. With the source term in the equation, computations revealed a rich structure which has been partially analyzed theoretically. Several problems for reaction diffusion equations in unbounded regimes were also investigated. It was shown that under certain conditions in the rate law all nonzero solutions blow up in finite time, while for other conditions in the rate law, solutions damp out.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1987
Accession Number
ADA189383

Entities

People

  • Howard A. Levine

Organizations

  • Iowa State University

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boundaries
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Convection
  • Differential Equations
  • Diffusion
  • Dynamics
  • Equations
  • Formulas (Mathematics)
  • Geometry
  • Inverse Problems
  • Mathematics
  • Partial Differential Equations
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.
  • Theoretical Analysis.