Analysis of Some Nonlinear Problems in Electromagnetic Fields

Washington State University, Pullman WA

Investigators

Abstract

NSF Award Abstract - DMS-0102261 Mathematical Sciences: Analysis of Some Nonlinear Problems in Electromagnetic Fields Abstract DMS-0102261 Hong-Ming Yin This project investigates several nonlinear problems arising from the theory of electromagnetic fields and heat conduction. The first problem area concerns investigation of induction heating processes. The mathematical model consists of nonlinear Maxwell's equations coupled with a nonlinear heat equation. The objective is to analyze whether or not thermal runaway (blowup) happens and how to prevent it if it does occur during a heating process. More complicated free boundary problems, modeling phase change during the heating process, are also under study. The second problem area concerns investigation of a p-Laplacian type of evolution system that models the classical Bean's critical-state model in the superconductivity theory. The effort focuses on understanding how the phase change takes place between normal and superconducting states. This project investigates mathematical models of heat flow in situations that involve electromagnetic fields. These models are important for many industrial applications. The results of this work will lead to a better understanding the complicated dynamics of electromagnetic fields and will provide explanations for certain experimental phenomena. In addition, this investigation will produce mathematical results of general interest for the study of Maxwell's equations and nonlinear heat conduction.