WELL-POSEDNESS OF WAVE EQUATION WITH A VARIABLE COEFFICIENT BY METHOD OF CHARACTERISTICS

Nao Nakagawa; Shintaro Yagi

doi:10.11948/20220325

2023 Volume 13 Issue 5

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Nao Nakagawa, Shintaro Yagi. WELL-POSEDNESS OF WAVE EQUATION WITH A VARIABLE COEFFICIENT BY METHOD OF CHARACTERISTICS[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2408-2415. doi: 10.11948/20220325

Citation:

Nao Nakagawa, Shintaro Yagi. WELL-POSEDNESS OF WAVE EQUATION WITH A VARIABLE COEFFICIENT BY METHOD OF CHARACTERISTICS[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2408-2415. doi: 10.11948/20220325

WELL-POSEDNESS OF WAVE EQUATION WITH A VARIABLE COEFFICIENT BY METHOD OF CHARACTERISTICS

Nao Nakagawa^1,,
Shintaro Yagi^2, ,

1.
Department of Electronic and Control Engineering, National Institute of Technology, Gifu College
2.
General Education, National Institute of Technology, Gifu College

Author Bio: Email: 2019d20@stu.gifu-nct.ac.jp(N. Nakagawa)
Corresponding author: Email: yagi@gifu-nct.ac.jp(S. Yagi)
Fund Project: The authors were supported by National Institute of Technology, Gifu College

Abstract

Abstract

This study proves well-posedness of wave equation with a variable coefficient in the Triebel-Lizorkin space $ F^s_{q, p} $ using the method of characteristics. Fourier series or transform cannot typically provide an explicit solution formula for equations with variable coefficients. Moreover, the theory presented by [16] on well-posedness in the $ L_q $ space is not suitable for problems in the $ F^s_{q, p} $ space. In this study, without using any solution formula and complex calculus, we describe the wave equation with variable coefficients as comprising ordinary differential equations in view of the theory of function spaces and method of characteristics.
- Wave equation /
- transport equation /
- ordinary differential equation /
- function analysis /
- method of characteristics
MSC: 35L05, 34A12, 35A24

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References

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