Lp-Convergence Rate to Nonlinear Diffusion Waves for p-System with Damping
By Kenji Nishihara, Weike Wang, Tong Yang. 2000
156 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/6355c98692718bae6850e450d383b6e5c7704fe6
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In Applied Mathematics
In Computational Theory and Mathematics
- Ming Mei
- Pierangelo Marcati
- Bruno Rubino
- Ronghua Pan
- Feimin Huang
- Zhen Wang
- Kenji Nishihara
- Zhian Wang
Citations in the corpus
- Lp-Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application (2003, background): “See also [9, 23 ,24,28] and the book [7] by Hsiao, and the references therein.”
- Nonlinear diffusion waves for hyperbolic p-system with nonlinear damping (2009, methodology): “Furthermore, by constructing an approximating Green function, Nishihara, Wang and Yang [19] and Wang and Yang [21] improved the rates as ‖(v − v̄, u − ū)(t)‖L∞ = O (1)(t−1, t−3/2), which is optimal in the sense comparing with the heat equation.”
- Stability of non-monotone critical traveling waves for reaction-diffusion equations with time-delay (2015, methodology): “To obtain such convergence rate result, to our best knowledge, the usual approaches are: either the monotone technology plus the optimal decay estimates on the corresponding linearized equations [16,18], or the Fourier’s transform plus energy estimates [10,21], or the approximate Green function meth”
- L1 Convergence to the Barenblatt Solution for Compressible Euler Equations with Damping (2011, background): “The conjecture mentioned above has been first justified by Hsiao and Liu in [13] and [14], and further improved by many mathematicians for small smooth or piecewise smooth solutions away from vacuum based on the energy estimates for derivatives; see [12], [15], [16], [17], [18], [30], [34], [35], [3”
- Convergence to nonlinear diffusion waves for a hyperbolic-parabolic chemotaxis system modelling vasculogenesis (2021, background): “1 come from [36] and [38], but additional efforts are needed to deal with the term g in (2.”
- Optimal Convergence Rates to Diffusion Waves for Solutions of the Hyperbolic Conservation Laws with Damping (2005, methodology): “But the method used in [17] is hard to extend to the IBVP case because of the difficulty of constructing a suitable approximating Green function.”