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- W4297576475 abstract "Consider the transmission eigenvalue problem for $u in H^1(Omega)$ and $vin H^1(Omega)$ 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 ${u_m, v_m}_{minmathbb{N}}$ associated with $k_mrightarrow+infty$ as $mrightarrow+infty$ such that the $L^2$-energies of $v_m$'s are concentrated around $partialOmega$. If $sigma$ and $mathbf{n}$ are both constant, we show the existence of transmission eigenfunctions ${u_j, v_j}_{jinmathbb{N}}$ such that both $u_j$ and $v_j$ are localized around $partialOmega$. 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." @default.
- W4297576475 created "2022-09-29" @default.
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- W4297576475 date "2022-01-22" @default.
- W4297576475 modified "2023-10-18" @default.
- W4297576475 title "Boundary localization of transmission eigenfunctions in spherically stratified media" @default.
- W4297576475 doi "https://doi.org/10.48550/arxiv.2201.08971" @default.
- W4297576475 hasPublicationYear "2022" @default.
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