Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations

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Hauptverfasser:	Kim, Seongyeon, Moon, Sunghwan, Seo, Ihyeok
Format:	Preprint
Veröffentlicht:	2023
Schlagworte:	Analysis of PDEs
Online-Zugang:	Acceder al recurso
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author	Kim, Seongyeon Moon, Sunghwan Seo, Ihyeok
author_facet	Kim, Seongyeon Moon, Sunghwan Seo, Ihyeok
contents	In this paper, we consider two types of damped wave equations: the weakly damped equation and the strongly damped equation. We recover the initial velocity from the trace of the solution on a space-time cylinder. This inverse problem is related to Photoacoustic Tomography (PAT), a hybrid medical imaging technique. PAT is based on generating acoustic waves inside of an object of interest and one of the mathematical problem in PAT is reconstructing the initial velocity from the solution of the wave equation measured on the outside of object. Using the spherical harmonics and spectral theorem, we demonstrate a way to recover the initial velocity.
format	Preprint
id	arxiv_https___arxiv_org_abs_2308_03362
institution	arXiv
publishDate	2023
record_format	arxiv
spellingShingle	Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations Kim, Seongyeon Moon, Sunghwan Seo, Ihyeok Analysis of PDEs In this paper, we consider two types of damped wave equations: the weakly damped equation and the strongly damped equation. We recover the initial velocity from the trace of the solution on a space-time cylinder. This inverse problem is related to Photoacoustic Tomography (PAT), a hybrid medical imaging technique. PAT is based on generating acoustic waves inside of an object of interest and one of the mathematical problem in PAT is reconstructing the initial velocity from the solution of the wave equation measured on the outside of object. Using the spherical harmonics and spectral theorem, we demonstrate a way to recover the initial velocity.
title	Reconstruction of the initial data from the trace of the solutions on an infinite time cylinder of damped wave equations
topic	Analysis of PDEs
url	https://arxiv.org/abs/2308.03362

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