Abstract

We study the Cauchy problem in the space of continuous functions for a nonlinear Sobolev type differential equation generalizing the equation of torsional vibrations of an infinite rod in a viscoelastic medium. Conditions for the existence of a global solution and for the blow-up of the solution of the Cauchy problem in finite time are considered.

中文翻译：

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粘弹性介质中杆扭转振动方程的柯西问题

摘要

我们研究了在非线性弹性Sobolev型微分方程的连续函数空间中的柯西问题，该方程泛化了粘弹性介质中无限杆的扭转振动方程。考虑了在有限时间内存在整体解和柯西问题解爆破的条件。