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Ide, K. and Kawashima, S. (2008) Decay Property of Regularity-Loss Type and Nonlinear Effects for Dissipative Timoshenko System. Mathematical Models and Methods in Applied Sciences, 18, 1001-1025.
https://doi.org/10.1142/s0218202508002930

has been cited by the following article:

• TITLE: The Global Existence of Smooth Solutions for Timoshenko-Cattaneo System with Two-Sound Waves in Besov Space

  AUTHORS: Xin’ai Fu

  KEYWORDS: Timoshenko-Cattaneo System, Regularity-Loss, Global Existence

  JOURNAL NAME: Advances in Pure Mathematics, Vol.15 No.4, April 15, 2025

  ABSTRACT: This paper is devoted to studying the global existence of smooth solutions for the Timoshenko-Cattaneo system with two sound waves. In the case of equal wave speeds and non-equal wave speeds, the Timoshenko-Cattaneo system exhibits regularity loss in the high-frequency part in order to obtain global well-posedness for the nonlinear Timoshenko-Cattaneo system with the minimum initial value of regularity index. This article applied harmonic analysis tools to establish the global solution for the Timoshenko-Cattaneo system in Besov space with a regularity index s= 3 2 .