## Abstract

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.

Original language | English |
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Pages (from-to) | 1591-1612 |

Number of pages | 22 |

Journal | Siam Journal on Applied Mathematics |

Volume | 53 |

Issue number | 6 |

Publication status | Published - Dec 1993 |

## Keywords

- MICROWAVE HEATING
- GINZBURG-LANDAU EQUATION
- SOLITON
- WAVE EQUATION
- HEAT EQUATION
- EQUATION