Upper bounds of blowup time for nonlinear extensible beam equations

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Abstract

This paper aims to investigate the initial boundary value problem for a class of Kirchhoff-type wave equations modified by Woinowsky-Krieger models, which can be used to describe the nonlinear extensible beam. Using the concave property of the function and a differential inequality, we estimate the upper bounds of the blowup time of the blowup solution at subcritical, critical, and high initial energy levels.

Keywords

extensible beam equation / Kirchhoff-type wave equation / upper bounds of the blowup time

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