三维空间中一类三阶双曲型方程的两个问题
Two Problems for One Hyperbolic Equation of the Third Order in Three-Dimensional Space
摘要：
本文用黎曼法求解了三阶双曲型方程的一个修正柯西问题（问题C），该问题的系数在奇平面上.引入了问题C的解具有更简单外形的特殊类，大大扩展了参数p进入方程的取值范围。在特殊类中，考虑了一类混合问题，其决策归结为二维一阶Volterra积分方程的不可约算子。作者发现了这些方程在不同参数p值下的唯一解。
英文摘要：
In the present article, a modified Cauchy problem (problem C) for the hyperbolic equation of the third order with the data on the equation's coefficients singularity plane is solved by Riemann method. The special class in which the solution of the problem C has more simple appearance is introduced and the area of values of the parameter p entering into the equation is considerably expanded. In the special class the mixed problem, which decision was been reduced to the two-dimensional Volterra's integral equations of the first order with uncurtailed operators, is considered. Authors found the unique solution of these equations at various values of the parameter p.
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