Blow-up analysis of coupled nonlinear parabolic equations with memory terms
Abstract
In this paper, we study the blow-up phenomena of the coupled nonlinear parabolic equations with nonlinear memory terms under non-homogeneous Neumann boundary conditions. By employing Kaplan's method, we construct blow-up subsolutions. This approach allows us to establish sufficient conditions for finite-time blow-up of solutions. Furthermore, we derive upper bounds for the blow-up time. Next, by constructing blow-up supersolutions and combining the auxiliary function method with modified differential inequality techniques, we derive lower bounds for the blow-up time. Finally, we provide two concrete examples to illustrate the theoretical results. Additionally, we employ the finite difference method to numerically simulate the equations and present figures to visually demonstrate the blow-up phenomenon.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Stability and Controllability of Differential Equations
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Communications on Pure & Applied Analysis
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 30
- Issue
- 0
- Pages
- 194–211
- Publication date
- 1 January 2026