# Blow-up Phenomena For Pseudo-Parabolic Kirchhoff Equations With Logarithmic Nonlinearity

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## Abstract

We consider pseudo-parabolic equations with $r(x)$-Kirchhoff coefficient and

logarithmic nonlinear term subject to Dirichlet boundary condions%

\begin{equation*}

\upsilon _{t}-\mu \Delta \upsilon _{t}-M(\left( \left\Vert \nabla \upsilon

\right\Vert _{r(x)}^{r(x)}\right) \Delta _{r(x)}\upsilon =\left\vert

\upsilon \right\vert ^{s(x)-2}\upsilon \ln \left\vert \upsilon \right\vert .

\end{equation*}%

Using a method based on differential inequalities, we prove that the

solutions become unbounded at a finite time $T$, and, we ascertain an upper

limit for this time in the case of negative initial energy. Additionally, we

determine a lower limit for the time at which blow-up occurs.

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*7*(2), 115–126. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/370

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