Partial differential equations and applications

Abstract

The PI proposes to continue his program to develop methods for the study of nonlinear deterministic and stochastic partial differential equations arising in natural and social sciences, engineering, etc. The emphasis is on nonlinear pde with rough time dependence (including stochastic fully nonlinear second-order and Hamilton-Jacobi equations, and conservation laws), random homogenization, adaptive dynamics and concentration phenomena in mathematical biology and equations on graphs/networks.In addition to the theoretical development the problems to be investigated arise as models in applications likecomposite materials, mean field games, turbulence, phase transitions and front propagation with random velocity, nucleations in physics, macroscopic limits of particle systems, pathwise stochastic control theory, stochastic optimization with partial observations, stochastic selection, turbulent combustion, phase transitions and front propagation in random media, cloaking, adaptive dynamics, data transmission and traffic management.

Document Details

Document Type
DoD Grant Award
Publication Date
Jan 04, 2017
Source ID
N000141712095

Entities

People

  • Panagiotis E. Souganidis

Organizations

  • Office of Naval Research
  • United States Navy
  • University of Chicago

Tags

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)