Local existence and finite time blow-up of solutions for a viscoelastic Kirchhoff-like plate equation with logarithmic source term
Abstract
Abstract In this paper, we study the initial-boundary value problem for a viscoelastic Kirchhoff-like plate equation with logarithmic source term. Based on the contraction mapping principle, we prove the local existence and uniqueness of solutions. By the concavity arguments, we obtain the finite time blow-up and estimates on the upper bound for the blow-up time of solutions with negative, null, positive, and arbitrary positive initial energy, respectively.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Nonlinear Partial Differential Equations
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- Advances in Nonlinear Analysis
- Publisher
- Walter de Gruyter GmbH
- Volume
- 15
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN