On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with stress-free condition
On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with stress-free condition
复制标题
DOI：
10.1090/qam/973382
复制
发表时间：
1988-12
影响因子：
0.8
通讯作者：
Takeyuki Nagasawa
中科院分区：
文献类型：
--
作者：
Takeyuki Nagasawa
(i-5> 6x（0，t）= dx（1，t）= 0。(1.6)这个问题是一个在真空中具有绝热端的多方理想气体的一维运动模型。（u，v，6），未知函数，表示气体的比容、速度和绝对温度;（R，n，Cy，k），给定正常数，分别表示气体常数、粘滞系数、定容热容和导热系数。条件（1.5）称为无应力条件。Kazhykhov在文献[2]中证明了该问题整体解的存在性，并构造了保持器类Dt>o^7+”xH 2 r + axH ^+"}（0 < a < 1）的解（u，v，6），条件是（wo，vq，Go）属于H1 + axH 2 + axH 2 +a. (For保持器空间Hn+a的定义等，见[3]。）我们称之为经典的解决方案在本文中。最近Okada [5]和Kawashima [1]证明了解的渐近性态。这个问题有一个微不足道的解决办法
(i-5> 6x{0,t) = dx{l,t) = 0. (1.6) This problem is a model of the one-dimensional motion of the polytropic ideal gas with adiabatic ends which is put into a vacuum. (u,v,6), unknown functions, represent the specific volume, the velocity, the absolute temperature of the gas; (R, n,Cy ,k), given positive constants, stand for the gas constant, the coefficient of viscosity, the heat capacity at constant volume, and the coefficient of heat conduction, respectively. The condition (1.5) is called the stress-free condition. Kazhykhov showed the global existence of a unique solution to this problem in [2], He constructed the solution (u,v,6) in the Holder class Dt>o^7+" x H2r+a x H^+"} (0 < a < 1) provided (wo, vq, Go) belongs to Hl+a x H2+a x H2+a. (For the definition of the Holder spaces Hn+a etc., see [3].) We call this solution classical in this paper. More recently Okada [5] and Kawashima [1] showed the asymptotic behavior of the solution. The problem has a trivial solution