Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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TIME PERIODIC SOLUTIONS TO A HEAT EQUATION WITH LINEAR FORCING AND BOUNDARY CONDITIONS

  • In-Jee Jeong (Department of Mathematics and RIM Seoul National University) ;
  • Sun-Chul Kim (Department of Mathematics Chung-Ang University)
  • Received : 2022.06.27
  • Accepted : 2022.12.02
  • Published : 2023.03.01
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Abstract

In this study, we consider a heat equation with a variable-coefficient linear forcing term and a time-periodic boundary condition. Under some decay and smoothness assumptions on the coefficient, we establish the existence and uniqueness of a time-periodic solution satisfying the boundary condition. Furthermore, possible connections to the closed boundary layer equations were discussed. The difficulty with a perturbed leading order coefficient is demonstrated by a simple example.

Keywords

Acknowledgement

I.-J. Jeong was supported by NRF-2022R1C1C1011051. S.-C. Kim was supported by NRF-2016R1D1A1B01007653.

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