Blow up and exponential growth for a pseudo-parabolic equation with p(x)-Laplacian and variable exponents. (April 2023)

• Record Type: Journal Article
• Authors: Di, Huafei; Qian, Xian; Peng, Xiaoming
• Is Part Of: Applied mathematics letters. Volume 138(2023)
• Publication Date: 2023-04
• Subjects: Pseudo-parabolic equation -- Finite time blow up -- Exponential growth -- Variable exponents -- p(x)-Laplacian; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2022.108517
• Languages: English
• ISSNs: 0893-9659

Abstract

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.