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中文摘要：
在给定的Sobolve空间中，研究了一类非线性弹性杆方程的初边值问题，其中非线性项具有临界增长指数。描述了考虑非线性势力作用下具有黏阻尼的弹性杆的振动问题，利用Faedo—Galerkin方法，通过对变系数及非线性的处理，证明了该系统在一定初边值条件下整体弱解的存在、唯一性。为此类力学振动问题的研究和计算提供了理论依据。
英文摘要：
The initial-boundary value problem was studied in given Sobolve space, where the nonlinear term satisfies a critical exponential growth condition. The problem involves a class of nonlinear partial differential equations describing the nonlinear elastic rods with viscous damp under external force. By using Faedo-Galerkin method, the existence and uniqueness of the weak solutions for the proposed problem were proved through the appropriate manipulation of variable coefficient and nonlinear items.
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