Given A, B in R^{n×n}, we consider the Cauchy problem for partially dissipative hyperbolic systems having the formwith the aim of providing a detailed description of the large-time behavior. Sharp Lp–Lqestimates, for 1 ≤q≤p≤∞, are established for the distance between the solution to the system and a time-asymptotic profile, where the profile is the superposition of diffusion waves and exponentially decaying waves. They show that the solution to the system decays to the diffusion waves 1/2faster than the diffusive decay rate (1/q−1/p)/2while the exponential decaying waves are negligible for large time. In particular, under a symmetry property, it decays 1faster than. The proof is based on a complex interpolation argument once Lrestimates for the fundamental solution to the system in the frequency space and Fourier multiplier estimates are accomplished.
Lp-Lq decay estimates for dissipative linear hyperbolic systems in 1D / Mascia, Corrado; Nguyen, Thinh Tien. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 263:10(2017), pp. 6189-6230. [10.1016/j.jde.2017.07.011]
Lp-Lq decay estimates for dissipative linear hyperbolic systems in 1D
Mascia, Corrado;
2017
Abstract
Given A, B in R^{n×n}, we consider the Cauchy problem for partially dissipative hyperbolic systems having the formwith the aim of providing a detailed description of the large-time behavior. Sharp Lp–Lqestimates, for 1 ≤q≤p≤∞, are established for the distance between the solution to the system and a time-asymptotic profile, where the profile is the superposition of diffusion waves and exponentially decaying waves. They show that the solution to the system decays to the diffusion waves 1/2faster than the diffusive decay rate (1/q−1/p)/2while the exponential decaying waves are negligible for large time. In particular, under a symmetry property, it decays 1faster than. The proof is based on a complex interpolation argument once Lrestimates for the fundamental solution to the system in the frequency space and Fourier multiplier estimates are accomplished.File | Dimensione | Formato | |
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