Boundary localization of transmission eigenfunctions in spherically stratified media
Boundary localization of transmission eigenfunctions in spherically stratified media
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球形分层介质中传输本征函数的边界定位
DOI：
10.3233/asy-221794
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发表时间：
2022-01
影响因子：
1.4
通讯作者：
Zhang Kai
中科院分区：
文献类型：
--
作者：
Jiang Yan;Liu Hongyu;Zhang Jiachuan;Zhang Kai
Consider the transmission eigenvalue problem for $u \\in H^1(\\Omega)$ and $v\\in H^1(\\Omega)$ associated with $(\\Omega; \\sigma, \\mathbf{n}^2)$, where $\\Omega$ is a ball in $\\mathbb{R}^N$, $N=2,3$. If $\\sigma$ and $\\mathbf{n}$ are both radially symmetric, namely they are functions of the radial parameter $r$ only, we show that there exists a sequence of transmission eigenfunctions $\\{u_m, v_m\\}_{m\\in\\mathbb{N}}$ associated with $k_m\\rightarrow+\\infty$ as $m\\rightarrow+\\infty$ such that the $L^2$-energies of $v_m$'s are concentrated around $\\partial\\Omega$. If $\\sigma$ and $\\mathbf{n}$ are both constant, we show the existence of transmission eigenfunctions $\\{u_j, v_j\\}_{j\\in\\mathbb{N}}$ such that both $u_j$ and $v_j$ are localized around $\\partial\\Omega$. Our results extend the recent studies in [15,16. Through numerics, we also discuss the effects of the medium parameters, namely $\\sigma$ and $\\mathbf{n}$, on the geometric patterns of the transmission eigenfunctions.
Consider the transmission eigenvalue problem for $u \\in H^1(\\Omega)$ and $v\\in H^1(\\Omega)$ associated with $(\\Omega; \\sigma, \\mathbf{n}^2)$, where $\\Omega$ is a ball in $\\mathbb{R}^N$, $N=2,3$. If $\\sigma$ and $\\mathbf{n}$ are both radially symmetric, namely they are functions of the radial parameter $r$ only, we show that there exists a sequence of transmission eigenfunctions $\\{u_m, v_m\\}_{m\\in\\mathbb{N}}$ associated with $k_m\\rightarrow+\\infty$ as $m\\rightarrow+\\infty$ such that the $L^2$-energies of $v_m$'s are concentrated around $\\partial\\Omega$. If $\\sigma$ and $\\mathbf{n}$ are both constant, we show the existence of transmission eigenfunctions $\\{u_j, v_j\\}_{j\\in\\mathbb{N}}$ such that both $u_j$ and $v_j$ are localized around $\\partial\\Omega$. Our results extend the recent studies in [15,16. Through numerics, we also discuss the effects of the medium parameters, namely $\\sigma$ and $\\mathbf{n}$, on the geometric patterns of the transmission eigenfunctions.
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DOI：
10.1080/03605302.2020.1843489
发表时间：
2019-05
影响因子：
1.9
作者：
F. Cakoni;Jingni Xiao
通讯作者：
F. Cakoni;Jingni Xiao
影响因子：
2.1
作者：
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H. Diao;Hongyu Liu;B. Sun
影响因子：
1.3
作者：
Hongyu Liu;Zaijiu Shang;Hongpeng Sun;J. Zou
通讯作者：
Hongyu Liu;Zaijiu Shang;Hongpeng Sun;J. Zou
影响因子：
2.1
作者：
Yuk-J Leung;D. Colton
通讯作者：
Yuk-J Leung;D. Colton
影响因子：
1.2
作者：
Hongyu Liu;J. Zou
通讯作者：
Hongyu Liu;J. Zou