Local well-posedness, global existence and blow-up for a heat equation with interior logarithmic source and nonlinear dynamic boundary condition
Abstract
In this article, a heat equation with an interior logarithmic source and a nonlinear dynamic boundary condition is considered. After establishing the local well-posedness, the global existence and finite time blow-up results of the solutions with different initial energy levels are given. Moreover, the lower bound of the maximal existence time of the weak solution is deduced for the special case $ m = 2 $.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Nonlinear Partial Differential Equations
Navier-Stokes equation solutions
Publication details
- Journal / source
- Communications in Analysis and Mechanics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 18
- Issue
- 1
- Pages
- 70–97
- Publication date
- 1 January 2026