一类线性双曲型方程Goursat问题的能量估计

Energy Estimation of Goursat Problems for A Class of Linear Hyperbolic Equation

在位势流模型下,研究了超音速气流过二维斜坡的弱激波解的存在唯一性.该问题的关键是证明其相应线性问题的先验能量估计.先通过部分速度图变换,将拟线性双曲方程的自由边值问题化简为固定边值问题,然后通过待定系数法,选择适当的积分因子,进行分部积分,结合问题本身的边界条件,获得了相应线性Goursat问题的能量估计.从而用相对简单的方法获得了与文献[1-2]类似的结果.

The local existence and uniqueness of weak shock solution in steady supersonic potential flow passing along a 2 - dimensional wedge were discussed. The free boundary problem was transferred to a fixed boundary problem by part-hodograph transform. Then by choosing a proper multiplier and integrating by parts, the energy estimation of the linear Goursat problem of the hyperbolic equation can be carried out in an easier way.