Abstract
Recently, a time-decay framework L2(Rn)∩B˙2,∞−s(Rn)(s>0) has been given by [49] for linearized dissipative hyperbolic systems, which allows to pay less attention to the traditional spectral analysis. However, owing to interpolation techniques, those decay results for nonlinear hyperbolic systems hold true only in higher dimensions (n≥3), and the analysis in low dimensions (say, n=1,2) was left open. We try to give a satisfactory answer in the current work. First of all, we develop new time-decay properties on the frequency-localization Duhamel principle, and then it is shown that the classical solution and its derivatives of fractional order decay at the optimal algebraic rate in dimensions n=1,2, by using a new technique which is the so-called “piecewise Duhamel principle” in localized time-weighted energy approaches compared to [49]. Finally, as direct applications, explicit decay statements are worked out for some relevant examples subjected to the same dissipative structure, for instance, damped compressible Euler equations, the thermoelasticity with second sound, and Timoshenko systems with equal wave speeds.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.