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Hölder regularity for the Moore-Gibson-Thompson equation with infinite delay

  • * Corresponding author

    * Corresponding author 
The first author is supported by the Project POSTDOC DICYT-041633LY at the USACH. The second author is partially supported by CONICYT, under Fondecyt Grant number 1140258 and and CONICYT - PIA - Anillo ACT1416. The third author is supported by the Basque Government through the BERC 2014-2017 program and by Spanish Ministry of Economy and Competitiveness MINECO: BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and GEAGAM, 644202 H2020-MSCA-RISE-2014.
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  • We characterize the well-posedness of a third order in time equation with infinite delay in Hölder 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 $g(t)=\frac{t^{ν-1}}{Γ(ν)}e^{-at}$ the third order problem is ill-posed whenever $0<ν ≤q 1$ and $a$ is inversely proportional to one of the terms of the given model.

    Mathematics Subject Classification: Primary:45N05;Secondary:45D05, 43A15.


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  • Figure 1.  Example of a parametric plot (${\mathfrak R}{\mathfrak e}\, \beta_2(\eta), {\mathfrak I}{\mathfrak m}\,\beta_2(\eta)$)

    Figure 2.  Example of a parametric plot (${\mathfrak R}{\mathfrak e}\, \beta_3(\eta), {\mathfrak I}{\mathfrak m}\,\beta_3(\eta)$)

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