部分耗散粘性平衡定律系统及其在库兹涅佐夫-韦斯特韦尔特方程中的应用

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Acta Applicandae Mathematicae Pub Date : 2024-09-25 DOI:10.1007/s10440-024-00686-7

Gilbert Peralta

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引用次数: 0

摘要

我们提供了在光滑 Sobolev 空间中部分耗散粘性平衡定律系统的好求解性，其假设条件与无粘性平衡定律的假设条件相同。利用弗里德里希正则化和莫瑟型估计，得出了具有有限正则系数的耦合双曲-抛物线性系统的先验估计。利用线性理论的结果和合适的迭代方案，将建立非线性系统的局部存在性。然后将局部存在性理论应用于非线性声波传播的库兹涅佐夫-韦斯特韦尔特带阻尼方程。建立了小数据全局解的存在性及其渐近稳定性。

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Partially Dissipative Viscous System of Balance Laws and Application to Kuznetsov–Westervelt Equation

We provide the well-posedness for a partially dissipative viscous system of balance laws in smooth Sobolev spaces under the same assumptions as in the case of inviscid balance laws. A priori estimates for coupled hyperbolic-parabolic linear systems with coefficients having limited regularity are derived using Friedrichs regularization and Moser-type estimates. Local existence for nonlinear systems will be established using the results of the linear theory and a suitable iteration scheme. The local existence theory is then applied to the Kuznetsov–Westervelt equation with damping for nonlinear wave acoustic propagation. Existence of global solutions for small data and their asymptotic stability are established.

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来源期刊

Acta Applicandae Mathematicae 数学-应用数学

CiteScore

2.80

自引率

6.20%

发文量

审稿时长

16.2 months

期刊介绍： Acta Applicandae Mathematicae is devoted to the art and techniques of applying mathematics and the development of new, applicable mathematical methods. Covering a large spectrum from modeling to qualitative analysis and computational methods, Acta Applicandae Mathematicae contains papers on different aspects of the relationship between theory and applications, ranging from descriptive papers on actual applications meeting contemporary mathematical standards to proofs of new and deep theorems in applied mathematics.