Abstract

The Cauchy problem for a system of nonlinear Volterra-type integral equations that describes, in Lagrangian coordinates, the motion of a finite mass of a rarefied self-gravitating gas bounded by a free surface is studied. A theorem of the existence and uniqueness of a solution to the problem in the space of infinitely differentiable functions is proved. The solution is constructed in the form of a series with recursively calculated coefficients. The local convergence of the series is proved using the method of successive approximations.

中文翻译：

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关于描述自重气体稀疏运动的积分方程组柯西问题解的存在唯一性

摘要

研究了非线性Volterra型积分方程组的柯西问题，该系统在拉格朗日坐标中描述了有限质量的，以自由表面为边界的稀有自重气体的运动。证明了在无穷微分函数空间中问题解的存在性和唯一性定理。该解决方案以具有递归计算系数的级数形式构造。使用逐次逼近的方法证明了该级数的局部收敛性。