9 (Sat.), 10 (Sun.), March, 2024

Room 111 (総合講義室2) at Faculty of Engineering Integrated Research Bldg. ([53] in map), Kyoto University.

I-Kun Chen (National Taiwan University)

Pu-Zhao Kow (National Chengchi University)

Yu-Chen Shu (National Cheng Kung University)

Jenn-Nan Wang (National Taiwan University)

Shih-Hsien Yu (Academia Sinica)

Hiroshi Fujiwara (Kyoto University) 藤原 宏志 (京都大学)

Hiroshi Isakari (Keio University) 飯盛 浩司 (慶應大学)

Masato Kimura (Kanazawa University) 木村 正人 (金沢大学)

Tomoyuki Miyaji (Kyoto University) 宮路 智行 (京都大学)

Hiroshi Takase (Kyushu University) 髙瀬 裕志 (九州大学)

**References**

[1] I.-K. Chen, H. Fujiwara, and D. Kawagoe, Tomography from scattered signals obeying the stationary radiative transport equation,

*Mathematics for Industry*

**37**(2023) pp.27-46

This research is an extension of previous studies[1, 2, 3], and is a joint work with J.-T. Li (Kanazawa U.), Y. Liu (Kyoto U.), G. Nakamura (Hokkaido U.), H. Notsu (Kanazawa U.), and Y. Ueda (Kobe U.).

**References**

[1] M. Kimura, H. Notsu, Y. Tanaka, and H. Yamamoto: The gradient flow structure of an extended Maxwell viscoelastic model and a structure-preserving finite element scheme. Journal of Scientific Computing, Vol.78 (2019) pp.1111-1131. doi:10.1007/s10915-018-0799-2

[2] J.-T. Li: Mathematical analysis of the Zener-type viscoelastic wave equation. Division of Mathematical and Physical Science, Graduate School of Natural Science and Technology, Kanazawa University, Master Thesis (2023 February).

[3] H. Yamamoto: Energy gradient flow structure of the Zener viscoelastic model and its finite element analysis. Master theis, Division of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology, Kanazawa University (February 2019) 36 pages (in Japanese).

**References**

[1] Geometric effects on $ W^{1, p} $ regularity of the stationary linearized Boltzmann equation arXiv preprint arXiv:2311.12387, 2023

**References**

[1] P. Chossat and M. Golubitsky, Iterates of maps with symmetry,

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[2] M. Golubitsky, I. Stewart, and D.G. Schaeffer,

*Singularities and Groups in Bifurcation Theory II*, Springer, New York, 1988.

[3] Y.A. Kuznetsov,

*Elements of Applied Bifurcation Theory*, Fourth edition Springer Nature, Switzerland, 2023.

[4] R. Mazrooei-Sebdani and Z. Eskandari, Neimark-Sacker Bifurcation with Zn-Symmetry and a Neural Application,

*Qual. Theory Dyn. Syst.*

**18**(2019) 931–946.

[5] K. Okamoto, T. Miyaji, and A. Tomoeda, Nonlinear delay difference equation with bistability as a new traffic flow model, submitted.

**References**

[1] M P Bendsøe and N Kikuchi 1988 Generating optimal topologies in structural design using a homogenization method

*Computer Methods in applied Mechanics and Engineering*

**71**(2) 197-224

[2] H Isakari K Kuriyama S Harada T Yamada T Takahashi and T Matsumoto 2014 A topology optimisation for three-dimensional acoustics with the level set method and the fast multipole boundary element method

*Mechanical Engineering Journal*

**1**(4) CM0039

[3] J Qin H Isakari K Taji T Takahashi and T Matsumoto 2021 A robust topology optimization for enlarging working bandwidth of acoustic devices

*International Journal for Numerical Methods in Engineering*

**122**(11) 2694-2711

[4] Y Honshuku and H Isakari 2022 A topology optimisation of acoustic devices based on the frequency response estimation with the Padé approximation

*Applied Mathematical Modelling*

**110**819-840

[5] J C Nédélec 2001 Acoustic and electromagnetic equations: integral representations for harmonic problems

**144**New York: Springer.

[6] S Amstutz and H Andrä 2006 A new algorithm for topology optimization using a levelset method.

*Journal of Computational Physics*

**216**(2) 573-588

**References**

[1] Q. Du, J. Yang, and Z. Zhou, 2020 Time-fractional allen{cahn equations: analysis and numerical methods,

*Journal of Scientific Computing*,

**85**, pp. 1-30

[2] T. Tang, H. Yu, and T. Zhou, 2019 On energy dissipation theory and numerical stability for time-fractional phase-field equations,

*SIAM Journal on Scientific Computing*,

**41**, pp. A3757-A3778

[3] H.-l. Liao, T. Tang, and T. Zhou, 2021 An energy stable and maximum bound preserving scheme with variable time steps for time fractional allen--cahn equation,

*SIAM Journal on Scientific Computing*,

**43**, pp. A3503-A3526.636

Some of the non-scattering domain can be constructed using partial balayage [1] or the minimizing problem (with free boundary) [2]. We also discuss the possible scattering and non-scattering behavior of an anisotropic and inhomogeneous Lipschitz medium, by connecting the anisotropic non-scattering problem to a Bernuolli type free boundary problem [3].

**References**

[1] P.-Z. Kow, S. Larson, M. Salo, and H. Shahgholian, Quadrature and nonscattering domains for the helmholtz equation, Potential Anal., 60 (2024), pp. 387–424. MR4696043, Zbl:7798456, doi:10.1007/s11118-022-10054-5. The results in the appendix are well-known, and the proofs can found at arXiv:2204.13934.

[2] P.-Z. Kow, M. Salo, and H. Shahgholian, A minimization problem with free boundary and its application to inverse scattering problems, arXiv preprint, (2023). arXiv:2303.12605. To appear in Interfaces Free Bound.

[3] , On scattering behavior of corner domains with anisotropic inhomogeneities, arXiv preprint, (2023). arXiv:2309.11213.

**References**

[1] A. Enciso, A. Shao, and B. Vergara. Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials.

*J. Eur. Math. Soc.*,

**23**(10):3459-3495, 2021.

[2] J. Vancostenoble. Lipschitz stability in inverse source problems for singular parabolic equations.

*Comm. Partial Differential Equations*,

**36**(8):1287-1317, 2011.

[3] J. Vancostenoble and E. Zuazua. Hardy inequalities, observability, and control for the wave and Schrödinger equations with singular potential.

*SIAM J. Math. Anal.*,

**41**(4):1508-1532, 2009.

Jenn-Nan Wang (National Taiwan University)

Yuusuke Iso (Kyoto University) 磯 祐介 (京都大学)

Hitoshi Imai (Doshisha University) 今井 仁司 (同志社大学)

Hiroshi Fujiwara (Kyoto University) 藤原 宏志 (京都大学)

Local Organizer

Daisuke Kawagoe (Kyoto University) 川越 大輔 (京都大学)