Given A, Bin R^n imes n, we consider the Cauchy problem for partially dissipative hyperbolic systems having the form partiatl_t u+Apartial_x u+Bu = 0, with the aim of providing a detailed description of the large-time behavior. Sharp Lp-Lq estimates are established for the distance between the solution to the system and a time-asymptotic profile, where the profile includes a solution to a parabolic system and a solution of a hyperbolic system. The key tools for the proof are the Fourier transform together with the Young inequality and the interpolation inequality.
Lp-Lq decay estimates for dissipative linear hyperbolic systems in 1d / Mascia, Corrado; Nguyen Tien, Thinh. - II:(2018), pp. 305-320. (Intervento presentato al convegno XVI International Conference on Hyperbolic Problems tenutosi a Aachen, Germany) [10.1007/978-3-319-91548-7_24].
Lp-Lq decay estimates for dissipative linear hyperbolic systems in 1d
Mascia Corrado;
2018
Abstract
Given A, Bin R^n imes n, we consider the Cauchy problem for partially dissipative hyperbolic systems having the form partiatl_t u+Apartial_x u+Bu = 0, with the aim of providing a detailed description of the large-time behavior. Sharp Lp-Lq estimates are established for the distance between the solution to the system and a time-asymptotic profile, where the profile includes a solution to a parabolic system and a solution of a hyperbolic system. The key tools for the proof are the Fourier transform together with the Young inequality and the interpolation inequality.| File | Dimensione | Formato | |
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