论文标题
非线性超声波中黑股方程的时间加权估计值
Time-weighted estimates for the Blackstock equation in nonlinear ultrasonics
论文作者
论文摘要
超声波旅行的高频引起了非线性现象。在热雾的流体中，它们是由黑色史托的声波方程捕获的，具有强阻尼。我们在这项工作中重新审视了其适当的分析。通过强烈的耗散，通过利用该方程式的抛物线样特征，我们构建了一个时间加权的能量框架来研究其局部溶解性。通过这种方式，与已知结果相比，在初始条件下，在限制性的规律性假设较低的情况下，我们在有限的域上获得了小数据。此外，我们证明了黑色Stock方程的这种初始边界值问题在全球范围内是可以解决的，并且它们的解决方案呈指数速度衰减至稳态。
High frequencies at which ultrasonic waves travel give rise to nonlinear phenomena. In thermoviscous fluids, these are captured by Blackstock's acoustic wave equation with strong damping. We revisit in this work its well-posedness analysis. By exploiting the parabolic-like character of this equation due to strong dissipation, we construct a time-weighted energy framework for investigating its local solvability. In this manner, we obtain the small-data well-posedness on bounded domains under less restrictive regularity assumptions on the initial conditions compared to the known results. Furthermore, we prove that such initial boundary-value problems for the Blackstock equation are globally solvable and that their solution decays exponentially fast to the steady state.
