Initial boundary value problem of pseudo‐parabolic Kirchhoff equations with logarithmic nonlinearity

• Published in: Mathematical methods in the applied sciences Vol. 47; no. 2; pp. 799 - 816
• Main Authors: Zhao, Qiuting, Cao, Yang
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 30.01.2024
• Subjects: blow‐up; Boundary value problems; Decay rate; global existence; logarithmic nonlinearity; Logarithms; Nonlinearity; pseudo‐parabolic Kirchhoff equation
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.9684

In this paper, we consider the initial boundary value problem for a pseudo‐parabolic Kirchhoff equation with logarithmic nonlinearity. Using the potential well method, we obtain a threshold result of global existence and finite‐time blow‐up for the weak solutions with initial energy J(u0)≤d$$ J\left({u}_0\right)\le d $$. When the initial energy J(u0)>d$$ J\left({u}_0\right)>d $$, we find another criterion for the vanishing solution and blow‐up solution. We also establish the decay rate of the global solution and estimate the life span of the blow‐up solution. Meanwhile, we study the existence of the ground state solution to the corresponding stationary problem.