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Comp."],"abstract":"<p>This paper considers the attenuated Westervelt equation in pressure formulation. The attenuation is by various models proposed in the literature and characterised by the inclusion of non-local operators that give power law damping as opposed to the exponential of classical models. The goal is the inverse problem of recovering a spatially dependent coefficient in the equation, the parameter of nonlinearity <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"kappa left-parenthesis x right-parenthesis\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mi>\u03ba<\/mml:mi>\n      <mml:mo stretchy=\"false\">(<\/mml:mo>\n      <mml:mi>x<\/mml:mi>\n      <mml:mo stretchy=\"false\">)<\/mml:mo>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">\\kappa (x)<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>, in what becomes a nonlinear hyperbolic equation with non-local terms. The overposed measured data is a time trace taken on a subset of the domain or its boundary. We shall show injectivity of the linearised map from <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"kappa\">\n  <mml:semantics>\n    <mml:mi>\u03ba<\/mml:mi>\n    <mml:annotation encoding=\"application\/x-tex\">\\kappa<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> to the overposed data and from this basis develop and analyse Newton-type schemes for its effective recovery.<\/p>","DOI":"10.1090\/mcom\/3683","type":"journal-article","created":{"date-parts":[[2021,7,28]],"date-time":"2021-07-28T13:58:00Z","timestamp":1627480680000},"page":"245-276","source":"Crossref","is-referenced-by-count":16,"title":["On an inverse problem of nonlinear imaging with fractional damping"],"prefix":"10.1090","volume":"91","author":[{"given":"Barbara","family":"Kaltenbacher","sequence":"first","affiliation":[]},{"given":"William","family":"Rundell","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2021,9,20]]},"reference":[{"issue":"5","key":"1","doi-asserted-by":"publisher","first-page":"658","DOI":"10.1134\/S0012266110050058","article-title":"A priori estimates for solutions of boundary value problems for equations of fractional order","volume":"46","author":"Alikhanov, A. 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