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

Author

Listed:
  • Yumei Liao

    (Department of Mathematics, School of Mathematics and Statistics, Guizhou University, Guiyang 550025, Guizhou, China
    Department of Mathematics, Guizhou Education University, Guiyang 550018, Guizhou, China)

  • Wei Wei

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

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.

Suggested Citation

  • Yumei Liao & Wei Wei, 2019. "The Regularity of Solution for Weakly Coupled System Derived by Microwave Heating Model," Mathematics, MDPI, vol. 7(6), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:501-:d:236556
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