非线性超声加热的耦合 Jordan-Moore-Gibson-Thompson-Pennes 模型的局部适定性
Local well-posedness of a coupled Jordan-Moore-Gibson-Thompson-Pennes model of nonlinear ultrasonic heating
AI总结：
本文研究了非线性超声加热的耦合 JMGT-Pennes 模型，利用能量法和不动点论证证明了在初始数据正则且较小、终时足够短的条件下模型的局部适定性。
摘要：
本文研究基于 Jordan-Moore-Gibson-Thompson 方程（JMGT）的非线性超声加热数学模型，该方程具有温度依赖的介质参数，并与用于生物热传递的半线性 Pennes 方程耦合。方程通过 JMGT 方程系数中的温度以及 Pennes 方程内的非线性源项耦合，该源项模拟周围组织对声能的吸收。利用能量法与不动点论证，我们证明在初始数据正则、在低阶拓扑中较小且终时足够短的情况下，该模型是局部适定的。
英文摘要：
In this work, we investigate a mathematical model of nonlinear ultrasonic heating based on the Jordan-Moore-Gibson-Thompson equation (JMGT) with temperature-dependent medium parameters coupled to the semilinear Pennes equation for the bioheat transfer. The equations are coupled via the temperature in the coefficients of the JMGT equation and via a nonlinear source term within the Pennes equation, which models the absorption of acoustic energy by the surrounding tissue. Using the energy method together with a fixed point argument, we prove that our model is locally well-posed, provided that the initial data are regular, small in a lower topology and the final time is short enough.
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