[2308.06968] Explicit inversion for variable-speed wave equations on bounded domains Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2308.06968 (math) [Submitted on 14 Aug 2023 ( v1 ), last revised 28 Apr 2026 (this version, v2)] Title: Explicit inversion for variable-speed wave equations on bounded domains Authors: Sunghwan Moon , Ihyeok Seo View a PDF of the paper titled Explicit inversion for variable-speed wave equations on bounded domains, by Sunghwan Moon and 1 other authors View PDF HTML (experimental) Abstract: We study the reconstruction of the initial pressure $f(x)=p(x,0)$ for the wave model \[ \partial_t^2 p(x,t)=c(x)\Delta_{x}p(x,t)\qquad (x,t)\in\Omega\times[0,\infty), \] posed on a bounded domain $\Omega$ with variable sound speed $c(\cdot)$. From time-resolved boundary measurements, we consider two settings: (i) measurement of $p|_{\partial\Omega\times[0,\infty)}$ under a Robin boundary condition $p+\alpha\,\partial_\nu p=0$ on $\partial\Omega\times[0,\infty)$ with $\alpha\gneq 0$, and (ii) measurement of $\partial_\nu p|_{\partial\Omega\times[0,\infty)}$ under a Dirichlet boundary condition $p=0$ on $\partial\Omega\times[0,\infty)$. Within a unified framework, we present explicit formulas that recover the spectral coefficients $\langle f,\phi_k^B\rangle$ of $f$ with respect to the eigenfunction bases of the operator $-c(\cdot)\Delta_{x}$ for boundary types $B\in\{D,R\}$. The framework integrates variable sound speed with Dirichlet/Robin boundary conditions in a single setting, enabling direct coefficient-level recovery from boundary data. Comments: To appear in Bull. Korean Math. Soc., 11 pages Subjects: Analysis of PDEs (math.AP) Cite as: arXiv:2308.06968 [math.AP] (or arXiv:2308.06968v2 [math.AP] for this version) https://doi.org/10.48550/arXiv.2308.06968 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ihyeok Seo [ view email ] [v1] Mon, 14 Aug 2023 07:06:26 UTC (9 KB) [v2] Tue, 28 Apr 2026 11:38:36 UTC (13 KB) Full-text links: Access Paper: View a PDF of the paper titled Explicit inversion for variable-speed wave equations on bounded domains, by Sunghwan Moon and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2023-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from