Abstract
We consider an initial–boundary value problem for the beam vibration equation, which is a fourth-order nonlinear equation with two independent variables. It is shown that under certain conditions on the initial data this problem can be reduced to the Cauchy problem for a countable system of quasilinear ordinary differential equations. Using the method of energy inequalities, we prove that this Cauchy problem has a solution. Based on this, we establish the existence of a local solution of the original initial–boundary value problem and construct it in closed form. A theorem on the uniqueness of a global solution is proved.
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Translated by V. Potapchouck
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Sabitov, K.B., Akimov, A.A. Initial–Boundary Value Problem for a Nonlinear Beam Vibration Equation. Diff Equat 56, 621–634 (2020). https://doi.org/10.1134/S0012266120050079
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DOI: https://doi.org/10.1134/S0012266120050079