Blow-up phenomena for a damped plate equation with logarithmic nonlinearity. (June 2023) - Li, Xiatong; Fang, Zhong Bo
Abstract: This paper is concerned with the finite time blow-up phenomena for a damped plate equation with logarithmic nonlinearity under the Navier boundary condition. Combining potential well method and modified differential inequality technique, we establish the finite time blow-up properties of solutions with low initial energy E ( 0 ) ≤ d and high energy. In particular, we consider the case where the initial displacement and initial velocity have the same ( ∫ Ω u 0 u 1 d x > 0 ) or different signs ( ∫ Ω u 0 u 1 d x > − ‖ u 0 ‖ ∗ 2 2 ) in the sense of L 2 inner product at high energy level. Moreover, the lower bounds for the blow-up time in subcritical, critical, supercritical and ultra-supercritical cases are also derived.