Global existence and blow-up of solution to a class of fourth-order equation with singular potential and logarithmic nonlinearity

Wu, Xiulan and Zhao, Yaxin and Yang, Xiaoxin (2023) Global existence and blow-up of solution to a class of fourth-order equation with singular potential and logarithmic nonlinearity. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2023 (55). pp. 1-16. ISSN 1417-3875

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Abstract

In this paper, we consider the well-posedness and asymptotic behavior of Dirichlet initial boundary value problem for a fourth-order equation with strong damping and logarithmic nonlinearity. We establish the local solvability by the technique of cut-off combining with the method of Faedo–Galerkin approximation. By means of potential well method and Rellich inequality, we obtain the global existence and the decay estimate of global solutions under some appropriate conditions. Furthermore, we prove the finite time blow-up results of weak solutions, and establish the upper and lower bounds for blow-up time.

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