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In this work, we investigate a mathematical model of nonlinear ultrasonicheating based on the Jordan-Moore-Gibson-Thompson equation (JMGT) withtemperature-dependent medium parameters coupled to the semilinear Pennesequation for the bioheat transfer. The equations are coupled via thetemperature in the coefficients of the JMGT equation and via a nonlinear sourceterm within the Pennes equation, which models the absorption of acoustic energyby the surrounding tissue. Using the energy method together with a fixed pointargument, we prove that our model is locally well-posed, provided that theinitial data are regular, small in a lower topology and the final time is shortenough.

Local well-posedness of a coupled Jordan-Moore-Gibson-Thompson-Pennes model of nonlinear ultrasonic heating