Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation

Korpela, JussiLassas, MattiOksanen, Lauri2021-02-192021-02-192019-06Korpela, J, Lassas, M & Oksanen, L 2019, 'Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation', Inverse problems and imaging, vol. 13, no. 3, pp. 575-596. https://doi.org/10.3934/ipi.2019027ORCID: /0000-0003-2043-3156/work/70954068http://hdl.handle.net/10138/326780An inverse boundary value problem for the 1+1 dimensional wave equation (partial derivative(2)(t) - c(x)(2)partial derivative(2)(x))u(x,t) = 0, x is an element of R+ is considered. We give a discrete regularization strategy to recover wave speed c(x) when we are given the boundary value of the wave, u(0,t), that is produced by a single pulse-like source. The regularization strategy gives an approximative wave speed (c) over tilde, satisfying a Holder type estimate parallel to (c) over tilde - c parallel to22engunspecifiedinfo:eu-repo/semantics/openAccessInverse problemregularization theorywave equationdiscretizationILL-POSED PROBLEMSNONLINEAR TIKHONOV REGULARIZATIONBANACH-SPACESRECONSTRUCTIONDIRICHLETSTABILITYRECOVERYUNIQUENESSALGORITHMTHEOREMMathematicsDiscrete regularization and convergence of the inverse problem for 1+1 dimensional wave equationArticleopenAccess1b365ad5-59da-4faa-b838-cb92d8b93e4585065722249000461762200007