The microwave heating of a material with temperature-dependent, nonohmic conductance is considered both analytically and analytically. In the case when the microwave amplitude is small, it is shown using a multiple scales expansion that the heating is governed by a Ginzburg-Landau type equation. This equation does not possess the solitary wave solutions of the full Ginzburg-Landau equation. Approximate solutions in the form of a slowly varying soliton and a front are found in certain parameter limits; these solutions compare very well with numerical solutions of the full governing equations. Initial-boundary value and initial value problems are considered numerically with particular emphasis on the structure of fronts.
|Number of pages||22|
|Journal||Siam Journal on Applied Mathematics|
|Publication status||Published - Dec 1993|
- MICROWAVE HEATING
- GINZBURG-LANDAU EQUATION
- WAVE EQUATION
- HEAT EQUATION