Infinite time blow‐up with arbitrary initial energy for a damped plate equation

Xiatong Li and Zhong Bo Fang

Mathematische Nachrichten, 2024, vol. 297, issue 6, 2148-2174

Abstract: This paper deals with the infinite blow‐up phenomena for a class of damped plate equations with logarithmic nonlinearity under the Navier boundary condition. Combining potential well method and modified differential inequality technique, we establish the infinite blow‐up result of solutions with arbitrary initial energy. In particular, it is not necessary to suppose that the initial velocity and the initial displacement should have the same sign in the sense of the L2${L^2}$ inner product, that is, the solution may blow up at infinity even ∫Ωu0u1dx −12u0∗2$\int _\Omega {{u_0}{u_1}dx} > - \frac{1}{2}\left\Vert {{u_0}} \right\Vert _*^2$.

Date: 2024
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https://doi.org/10.1002/mana.202300275

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