论文标题
具有热和分子松弛的无粘性介质中非线性声波的渐近行为
Asymptotic behavior of nonlinear sound waves in inviscid media with thermal and molecular relaxation
论文作者
论文摘要
通过热和分子弛豫的培养基传播的超声传播可以通过时间非线性波样方程在带有内存的时间内建模。本文在所谓的关键案例中调查了这种模型的凯奇问题的渐近行为，即非局部约旦 - 莫尔 - 吉布森 - 汤普森方程，这对应于无粘性流体中的传播。记忆具有指数式褪色的特征和I型，这意味着仅涉及声速电位。全球分析中的一个主要挑战是线性化方程的衰减估计值是规则性损失类型。结果，经典的能量方法无法用于非线性问题。为了克服这一困难，我们构建了适当的时间加权规范，其中权重可以具有负数。这些有问题的规范创建了人工阻尼术语，有助于控制非线性和衍生物的丧失，并最终使我们能够发现该模型的渐近行为。
Ultrasonic propagation through media with thermal and molecular relaxation can be modeled by third-order in time nonlinear wave-like equations with memory. This paper investigates the asymptotic behavior of a Cauchy problem for such a model, the nonlocal Jordan--Moore--Gibson--Thompson equation, in the so-called critical case, which corresponds to propagation in inviscid fluids. The memory has an exponentially fading character and type I, meaning that involves only the acoustic velocity potential. A major challenge in the global analysis is that the linearized equation's decay estimates are of regularity-loss type. As a result, the classical energy methods fail to work for the nonlinear problem. To overcome this difficulty, we construct appropriate time-weighted norms, where weights can have negative exponents. These problem-tailored norms create artificial damping terms that help control the nonlinearity and the loss of derivatives, and ultimately allow us to discover the model's asymptotic behavior.
