守恒双曲型方程式初边值问题的隐式解及一维情形下激波稀疏波的确定

１　一维守恒双曲型标量方程的初边值问题解法讨论一维标量守恒双曲型方程　ｕｔ＋ｆ（ｕ）ｘ＝０（１）的纯初值问题　ｕ（ｘ，０）＝φ１（ｘ）（－∞＜ｘ＜∞）（２）及初边值问题　ｕ（ｘ，０）＝φ１（ｘ），（０≤ｘ＜∞）　ｕ（０，ｔ）＝φ２（ｔ）（０≤ｔ＜∞）（３）并得到如下结果：１）问题（１），（２）当１＋ｆ″φ１′ｔ≠０时的隐式解为　ｕ（ｘ，ｔ）＝φ１（ｘ－ｆ′（ｕ（ｘ，ｔ））ｔ）（４）２）问题（１），（３）当１＋φ′１ｆ″ｔ≠０，１－φ２′ｘｆ″／（ｆ′）２≠０时的解为　ｕ（ｘ，ｔ）＝φ１（ｘ－ｆ′…

The Implicit Solution of the Conservative Hyperbolic Systems and the Determination of the Shock and Rarefaction Wave

Theim plicitsolutionsoftheinitial-boundary value conservativehyperbolic problem are suggested and solved by the algebraic iterative m ethod num erically. This can be used in the solution ofthe sm ooth partfor the hyperbolic system to som e extent. By the geo- m etric m ethod, the position of the shock and rarefaction w ave for the scalar conservative hy- perbolic equation is determ inated.