Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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WEAK SOLUTION OF AN ARCH EQUATION ON A MOVING BOUNDARY

  • DAEWOOK KIM (Department of Mathematics Education, Seowon University) ;
  • SUDEOK SHON (Department of Architectural Engineering, KOREATECH) ;
  • JUNHONG HA (School of Liberal Arts, KOREATECH)
  • Received : 2023.08.21
  • Accepted : 2023.10.12
  • Published : 2024.01.30
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Abstract

When setting up a structure with an embedded shallow arch, there is a phenomenon where the end of the arch moves. To study the so-called moving domain problem, one try to transform a considered noncylindrical domain into the cylindrical domain using the transform operator, as well as utilizing the method of penalty and other approaches. However, challenges arise when calculating time derivatives of solutions in a domain depending on time, or when extending the initial conditions from the non-cylindrical domain to the cylindrical domain. In this paper, we employ the transform operator to prove the existence and uniqueness of weak solutions of the shallow arch equation on the moving domain as clarifying the time derivatives of solutions in the moving domain.

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Acknowledgement

D. Kim was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2021R1F1A1047079).

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