Lp ENERGY METHOD FOR MULTI-DIMENSIONAL VISCOUS CONSERVATION LAWS AND APPLICATION TO THE STABILITY OF PLANAR WAVES
Lp ENERGY METHOD FOR MULTI-DIMENSIONAL VISCOUS CONSERVATION LAWS AND APPLICATION TO THE STABILITY OF PLANAR WAVES
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DOI：
10.1142/s0219891604000196
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发表时间：
2004-09
影响因子：
0.7
通讯作者：
S. Kawashima;S. Nishibata;Masataka Nishikawa
中科院分区：
文献类型：
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作者：
S. Kawashima;S. Nishibata;Masataka Nishikawa
我们引入了一种新的多维粘性守恒定律的 Lp 能量方法。我们的能量方法足以导出柯西问题 W1,p 空间中解的最佳衰减估计。它也适用于全空间或半空间中平面波的稳定性问题，并给出了随着时间趋于无穷大，平面波的最优收敛速度。这种能量方法利用了几个特殊的插值不等式。
We introduce a new Lp energy method for multi-dimensional viscous conservation laws. Our energy method is useful enough to derive the optimal decay estimates of solutions in the W1,p space for the Cauchy problem. It is also applicable to the problem for the stability of planar waves in the whole space or in the half space, and gives the optimal convergence rate toward the planar waves as time goes to infinity. This energy method makes use of several special interpolation inequalities.