Global Existence and Some Qualitative Properties of Weak Solutions for a Class of Heat Equations with a Logarithmic Nonlinearity in Whole \({\mathbb {R}}^{N}\)

This paper aims to investigate the global existence and uniqueness of weak solutions for a class of heat equations with logarithmic nonlinearity in \({\mathbb {R}}^{N}\) ${\mathbb{R}}^N$ , as well as to examine some of their qualitative properties. Additionally, we analyze the boundedness and higher integrability of these solutions.