The Regularity of Solution for Weakly Coupled System Derived by Microwave Heating Model

Yumei Liao and Wei Wei
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Yumei Liao: Department of Mathematics, School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China
Wei Wei: Department of Mathematics, School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China

Mathematics, 2019, vol. 7, issue 6, 1-11

Abstract: In this paper, we study the regularity of the weak solution of the coupled system derived from the microwave heating model with frequency variable. We first show that the weak solution E of the system is Hölder continuous near the boundary of S = ∂ Ω . The main idea of the proof is based on the estimation of linear degenerate system in Campanato space. Then we show that the solution u of the heat conduction equation is Hölder continuous with exponent α 2 . Finally, under the appropriate conditions we show that the coupled system with microwave heating has a weak solution. Moreover the regularity of the weak solution is studied.

Keywords: time-harmonic Maxwell’s equations; microwave heating model; regularity of weak solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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