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

Liao, Yumei; Wei, Wei

doi:10.3390/math7060501

Open AccessArticle

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

by

Yumei Liao

^1,2

and

Wei Wei

^1,3,*

¹

Department of Mathematics, School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China

²

Department of Mathematics, Guizhou Education University, Guiyang 550018, Guizhou, China

³

Department of Mathematics, Guizhou Minzu University, Guiyang 550025, Guizhou, China

^*

Author to whom correspondence should be addressed.

Mathematics 2019, 7(6), 501; https://doi.org/10.3390/math7060501

Submission received: 11 April 2019 / Revised: 23 May 2019 / Accepted: 28 May 2019 / Published: 2 June 2019

Download Versions Notes

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 = \partial 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

\frac{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

Share and Cite

MDPI and ACS Style

Liao, Y.; Wei, W. The Regularity of Solution for Weakly Coupled System Derived by Microwave Heating Model. Mathematics 2019, 7, 501. https://doi.org/10.3390/math7060501

AMA Style

Liao Y, Wei W. The Regularity of Solution for Weakly Coupled System Derived by Microwave Heating Model. Mathematics. 2019; 7(6):501. https://doi.org/10.3390/math7060501

Chicago/Turabian Style

Liao, Yumei, and Wei Wei. 2019. "The Regularity of Solution for Weakly Coupled System Derived by Microwave Heating Model" Mathematics 7, no. 6: 501. https://doi.org/10.3390/math7060501

APA Style

Liao, Y., & Wei, W. (2019). The Regularity of Solution for Weakly Coupled System Derived by Microwave Heating Model. Mathematics, 7(6), 501. https://doi.org/10.3390/math7060501

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

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

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI