doi:10.3934/cpaa.2018015engAbadías Ullod, LucianoLizama, CarlosMurillo-Arcila, MarinaHölder regularity for the Moore-Gibson-Thompson equation with infinite delayART-2018-106682We characterize the well-posedness of a third order in time equation with infinite delay in Ho ¨lder spaces, solely in terms of spectral properties concerning the data of the problem. Our analysis includes the case of the linearized Kuznetzov and Westerwelt equations. We show in case of the Laplacian operator the new and surprising fact that for the standard memory kernel g(t) = t¿-1 e-at the third order problem is ill-posed whenever 0 < ¿ = 1 and a is inversely G(¿ ) proportional to the damping term of the given model.2018http://zaguan.unizar.es/record/13114610.3934/cpaa.2018015http://zaguan.unizar.es/record/131146oai:zaguan.unizar.es:131146info:eu-repo/grantAgreement/EC/H2020/644202/EU/Geophysical Exploration using Advanced GAlerkin Methods/GEAGAMThis project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No H2020 644202-GEAGAMCOMMUNICATIONS ON PURE AND APPLIED ANALYSIS 17, 1 (2018), 243-265by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess