Blow up and exponential growth for a pseudo-parabolic equation with p(x)-Laplacian and variable exponents. (April 2023) - Di, Huafei; Qian, Xian; Peng, Xiaoming
Abstract: Considered herein is the initial–boundary value problem for the pseudo-parabolic equation u t − Δ u t − div | ∇ u | p ( x ) − 2 ∇ u + ω | u | m ( x ) − 2 u t = b | u | r ( x ) − 2 u . We first give a finite time blow up criterion and then establish upper bound estimate of blow up time. In addition, we investigate the exponential growth rate of the solutions under certain conditions.