具有非线性阻尼和Neumann及吸收边界条件的Westerpyruvate方程解的局部存在性
Local existence results for the Westervelt equation with nonlinear damping and Neumann as well as absorbing boundary conditions
摘要：
研究了具有非线性阻尼项、低阶阻尼项、Neumann边界条件和吸收边界条件的Westerpyruvate方程。在初值和边界条件充分小的假设下，证明了该方程的弱解在时间上的局部存在性。此外，我们证明了局部适定性的情况下，空间变化的$L^{\infty}$系数，模型相关的高强度聚焦超声（HIFU）的应用。
英文摘要：
We investigate the Westervelt equation with several versions of nonlinear damping and lower order damping terms and Neumann as well as absorbing boundary conditions. We prove local in time existence of weak solutions under the assumption that the initial and boundary data are sufficiently small. Additionally, we prove local well-posedness in the case of spatially varying $L^{\infty}$ coefficients, a model relevant in high intensity focused ultrasound (HIFU) applications.
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