[1]易菊燕.带退化粘性项的单个守恒律一般初边值问题的解的L~p-收敛率[J].江西师范大学学报(自然科学版),2012,(04):350-354.
 YI Ju-yan.The Lp-Convergence Rate for Initial-Boundary Value Problem of Scalar Conservation Law with Degenerate Viscosity[J].,2012,(04):350-354.
点击复制

带退化粘性项的单个守恒律一般初边值问题的解的L~p-收敛率()
分享到:

《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2012年04期
页码:
350-354
栏目:
出版日期:
2012-08-01

文章信息/Info

Title:
The Lp-Convergence Rate for Initial-Boundary Value Problem of Scalar Conservation Law with Degenerate Viscosity
作者:
易菊燕
暨南大学数学系,广东 广州 510632
Author(s):
YI Ju-yan
关键词:
退化粘性项一般初边值问题稀疏波L1-估计衰减估计
Keywords:
degenerate viscosity general initial-boundary value problem rarefaction wave L1-estimate decay rate
分类号:
O175.27
文献标志码:
A
摘要:
在半空间中讨论具有一般边界的带退化粘性项的单个守恒律初边值问题的解的收敛率.在流函数为凸条件下,使用 L1-估计导出了解渐近衰减到稀疏波的1个 Lp-衰减估计,从而澄清了一般边界条件对衰减率的影响.
Abstract:
It is concerned with convergence rates toward the rarefaction waves of the solutions of the initial boundary data problem for scalar conservation law with degenerate viscosity and the general boundary data. Under the condition of convex flux, using L1-estimate derives a Lp-decay rate of the rarefaction wave for scalar conservation law with degenerate viscosity. From this decay rate estimate, the effect of the general boundary data on the decay rate is clarified.

参考文献/References:

[1] Harabetian E. Rarefactions and large time behavior for parabolic equations and monotone schemes [J]. Commum Math Phys, 1988, 114(4): 527-536.
[2] II’in A M, Oleinik O A. Behavior of the solution of the Cauchy problem for certain quasilinear equations for unbounded increase of the time [J]. AMS Transl, 1964, 42(2): 19-23.
[3] Kawashima S, Nishibata S, Nishikawa M. Asymptotic stability of stationary waves for two-dimensional viscous conservation laws in half space [J]. Discrete and Continuous Dynamical Systerms, 2003(1): 469-476.
[4] Xu Yanling, Jiang Mina. Asymptiotic stability of rarefaction wave for generalized Burgers equation [J]. Acta Math Sci, 2005, 25B(1): 119-129.
[5] Chen Jing, Zhu Changjiang. Decay rates of strong planar rarefaction waves to scalar conservation laws with degenerate viscosity in several dimensions [J]. Trans Amer Math Soc, 2010, 362(4): 1797-1830.
[6] Feng Ruirui, Li Hailing, Zhong Weiming. L2-decay rate to rarefaction waves for general initial-boundary value probelm of scalar viscous conservation laws [J]. Far East Journal of Math Sci, 2010, 42(2): 205-218.
[7] Hattori Y, Nishihara K. A note on the stability of the rarefaction wave of the Burgers equation [J]. Japan J Indust Appl Math, 1991, 8(1): 85-96.
[8] Ito K. Asymptotic decay toward the planar rarefaction waves of solutions for viscous conservation laws in several space dimensions [J]. Math Models Methods Appl Sci, 1996, 6(3): 315-338
[9] Nakamura T. Asymptotic decay toward the rarefaction waves of solutions for viscous conservations laws in a one–dimensional half space [J]. SIAM J Math Anal, 2003, 34(6): 1308-1317.

更新日期/Last Update: 1900-01-01