Research on Deterministic and Stochastic Partial Differential Equations with Applications to Continuum Physics and Stochastic Systems Modelling

Abstract

This is a summary of research done by four senior investigators. Dafermos' research focused on a number of problems that lie at the interface of continuum mechanics and analysis. Fleming's research was concerned with optimal stochastic control theory, nonlinear filtering, large deviations for Markov diffusions, and viscosity solutions of nonlinear partial differential equations. Kushner's research covered a wide range of topics in stochastic systems theory and applied probability. Souganidis worked in the area of first and second order nonlinear partial differential equations, where a number of results concerning approximations with error estimates, singular perturbations and representation formulae were found. He also worked on questions of stability of special solutions of equation in fluids, as well as the structure of solutions of equations describing flows through porous media (implosion of waves).

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Document Details

Document Type
Technical Report
Publication Date
Jun 30, 1988
Accession Number
ADA206907

Entities

People

  • Wendell Fleming

Organizations

  • Brown University

Tags

Communities of Interest

  • Energy and Power Technologies
  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Asymptotic Series
  • Control Systems
  • Differential Equations
  • Dynamic Programming
  • Equations
  • Filters
  • Filtration
  • Markov Processes
  • Materials
  • Mathematical Filters
  • Mechanics
  • Partial Differential Equations
  • Probability
  • Signal Processing
  • Stochastic Control

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)