Existence of solutions for a model of microwave heating

Pierluigi Colli; Luca  Scarpa

doi:10.3934/dcds.2016.36.3011

Article Contents

2016, Volume 36, Issue 6: 3011-3034. Doi: 10.3934/dcds.2016.36.3011

This issue Previous Article A degenerate edge bifurcation in the 1D linearized nonlinear Schrödinger equation Next Article Bubbling on boundary submanifolds for a semilinear Neumann problem near high critical exponents

Existence of solutions for a model of microwave heating

Pierluigi Colli^1, and
Luca Scarpa^2,

1.
Dipartimento di Matematica "F. Casorati", Università di Pavia, Via Ferrata 1, 27100 Pavia
2.
Department of Mathematics, University College London, Gower Street, London WC1E 6BT

Received: June 2015

Revised: October 2015

Published: May 2017

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Abstract

This paper is concerned with a system of differential equations related to a circuit model for microwave heating, complemented by suitable initial and boundary conditions. A RLC circuit with a thermistor is representing the microwave heating process with temperature-induced modulations on the electric field. The unknowns of the PDE system are the absolute temperature in the body, the voltage across the capacitor and the electrostatic potential. Using techniques based on monotonicity arguments and sharp estimates, we can prove the existence of a weak solution to the initial-boundary value problem.

Keywords:

Microwave heating,
circuit model,
evolutionary system of partial differential equations,
weak solution,
global existence.

Mathematics Subject Classification: Primary: 35G61, 34A10, 35D30, 35Q79.

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