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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2023; 60(2): 465-477

Online first article February 20, 2023      Printed March 1, 2023

https://doi.org/10.4134/JKMS.j220317

Copyright © The Korean Mathematical Society.

Time periodic solutions to a heat equation with linear forcing and boundary conditions

In-Jee Jeong, Sun-Chul Kim

Seoul National University; Chung-Ang University

Abstract

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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: Parabolic equation, time periodic solution, closed boundary layer

MSC numbers: Primary 35K05; Secondary 76D10

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

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