entropy inequality meaning in English
熵不等式
Examples
- In the fields of fluid dynamics , entropy inequality reflects the second law of thermodynamics . i . e . . entropy must increase across shock waves ( a kind of discontinuity ) . all kind of approximate schemes should reflect the fact that it must satisfies some kind of discrete entropy inequality ) . from the view of practical computation , stability and theo - retical error of any kind discrete schemes all dependend of the smoothness of the solution of ( 0 . 2 . 1 ) . generally , the approximate solution have good stability and theoretial error in the area where the solutions have more regularity and poor stability and theoretial error in other area
从流体力学来看，它事实上是热力学第二定理的反映，即熵越过激波(一种间断)要增加。各种估计格式构造的估计解应反映这一事实，即满足熵不等式。从实际计算来看，总是通过离散化求解，不考虑计算的积累误差，它的稳定性与计算精度都依赖与真解的光滑性，一般说，在解较光滑的区域有较好的稳定性与计算精度，而在较粗糙的区域则相反。 - Due to the poor regularity of solutions at large time . ( 0 . 2 . 1 ) can not defined in classical way . i , e . , the defi nition of the derivatives at any points has no sense . so it may be rather difficult in the research of classical way and must be defined in weak sense . in order to guarantee the uniqueness of weak solutions , a condition ( entropy inequality ) must be need to pick out " good " solution ( entropy solutions )
由于大时间范围内守恒律( 0 . 1 . 1 )的解表现为很差的正则性，它不能在古典意义下定义，即在每一点下的导数无意义，使得古典办法研究遇到很大困难，它只能在弱意义下定义弱解，但往往这种弱解不唯一，需要某条件限制确保解的唯一性，在数学上称为熵条件，满足该条件的弱解称为熵解。