@article{Liu2026, 
author = {Dengming Liu and Fang He and Qi Chen},
title = {Local well-posedness, global existence and blow-up for a heat equation with interior logarithmic source and nonlinear dynamic boundary condition},
year = {2026},
journal = {Communications in Analysis and Mechanics},
volume = {18},
number = {1},
pages = {70-97},
keywords = {local well-posedness, global existence, blow-up, logarithmic nonlinearity source, nonlinear dynamic boundary condition},
url = {https://www.sciopen.com/article/10.3934/cam.2026003},
doi = {10.3934/cam.2026003},
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.}
}