Time-fractional Moore–Gibson–Thompson equations
Copyright policy )Time-fractional Moore–Gibson–Thompson equations
In this paper, we consider several time-fractional generalizations of the Jordan–Moore–Gibson–Thompson (JMGT) equations in nonlinear acoustics as well as their linear Moore–Gibson–Thompson (MGT) versions. Following the procedure described in Jordan (2014), these time-fractional acoustic equations are derived from four fractional versions of the Maxwell–Cattaneo law in Compte and Metzler (1997). Additionally to providing well-posedness results for each of them, we also study the respective limits as the fractional order tends to one, leading to the classical third order in time (J)MGT equation.
- Radboud University Nijmegen Netherlands
- University of Klagenfurt Austria
nonlinear acoustics, Maxwell-Cattaneo law, Hydro- and aero-acoustics, Fractional partial differential equations, 35L05, 35L72, Mathematics - Analysis of PDEs, Second-order quasilinear hyperbolic equations, well-posedness, FOS: Mathematics, fractional MGT equations, limiting behavior, Mathematics, Analysis of PDEs (math.AP)
nonlinear acoustics, Maxwell-Cattaneo law, Hydro- and aero-acoustics, Fractional partial differential equations, 35L05, 35L72, Mathematics - Analysis of PDEs, Second-order quasilinear hyperbolic equations, well-posedness, FOS: Mathematics, fractional MGT equations, limiting behavior, Mathematics, Analysis of PDEs (math.AP)
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