This article deals with Euler–Bernoulli beam type equation subject to initial and boundary conditions. Semigroup theory of bounded linear operators, Rothe’s time-discretization method and Gronwall’s inequality are used to establish approximate solutions, and proved the existence of a unique strong solution. Some error estimates have also been discussed. An example is provided to illustrate the main result.

中文翻译：

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Euler-Bernoulli 梁类型方程的近似解

本文处理受初始和边界条件约束的 Euler-Bernoulli 梁型方程。利用有界线性算子的半群理论、Rothe 时间离散化方法和Gronwall 不等式建立近似解，证明了唯一强解的存在性。还讨论了一些误差估计。提供了一个例子来说明主要结果。