A class of fourth-order parabolic systems with time dependent coefficients with blow-up solutions
Abstract
This paper deals with a class of initial-boundary value problems for nonlinear fourth-order parabolic systems with time dependent coefficients in a bounded domain. We establish conditions on the shape of the spatial domain and on data sufficient to guarantee that the solution blows up in finite time $ t^* $, deriving an upper bound for $ t^* $. Moreover, by introducing suitable conditions on the source terms, we obtain a lifespan of the solution, i.e. a time interval $ [0, T], $ where the solution exists and remains bounded, by deriving a lower bound $ T $ of the blow-up time $ t^* $.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Differential Equations and Boundary Problems
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - S
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 28
- Issue
- 0
- Pages
- 129–138
- Publication date
- 1 January 2026
- Language
- EN