Date of Award

Spring 2011

Document Type


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Gregory A. Kriegsmann

Second Advisor

Gerald Martin Whitman

Third Advisor

Michael R. Booty

Fourth Advisor

Peter G. Petropoulos

Fifth Advisor

Richard O. Moore


Two-dimensional reaction diffusion equations, which contain a functional and an inhomogeneous source term, are good models for describing microwave heating of thin ceramic slabs and cylinders in a multi mode, highly resonant cavity. A thin ceramic slab situated in a TEN03 rectangular cavity modeled in the small Biot number limit and a thin silicon wafer situated in a TM101 cylindrical cavity modeled in the small fineness ratio limit are studied to gain insight into the dynamics of the heating process. The evolution of temperature is governed by a two-dimensional reaction diffusion equation and a spatially non-homogeneous reaction term. Numerical methods are applied to accurately approximate the steady state leading order temperature of this equation and to determine the stability of solutions for Neumann boundary conditions. The choices of parameters in the equation that lead to uniform heating of the ceramic slab have been characterized.

Included in

Mathematics Commons