Existence of solutions for a model of microwave heating

TL;DR

This paper proves the existence of weak solutions for a PDE system modeling microwave heating involving an RCL circuit with a thermistor, using monotonicity and estimate techniques.

Contribution

It introduces a mathematical framework demonstrating the existence of solutions for a complex microwave heating model with temperature-dependent effects.

Findings

Existence of weak solutions established

Mathematical techniques based on monotonicity used

Model captures temperature and electric field interactions

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 RCL 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.