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• W3106814752 abstract "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." @default.
• W3106814752 created "2020-12-07" @default.
• W3106814752 creator A5001203951 @default.
• W3106814752 creator A5026093634 @default.
• W3106814752 date "2020-12-02" @default.
• W3106814752 modified "2023-09-27" @default.
• W3106814752 title "Asymptotic behavior of nonlinear sound waves in inviscid media with thermal and molecular relaxation" @default.
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• W3106814752 hasPublicationYear "2020" @default.
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