Existence and stability of a one-dimensional heat equation with logarithmic nonlinearity

• Published in: Journal of inequalities and applications Vol. 2025; no. 1; pp. 22 - 14
• Main Authors: Sun, Cong, Jiang, Yan Zhuo
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 25.02.2025; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Boundary value problems; Exponential decay to zero; Exponential stability; Global solution; Heat equation; Logarithms; Mathematics; Mathematics and Statistics; Nonlinearity; Partial differential equations; Stability; Thermodynamics; Exponential decay to zero; Heat equation; Exponential stability; Global solution

This paper deals with the existence and stability of the solution for a class heat equation with logarithmic nonlinearity. Using the potential well method, we proved the existence of global solutions. Moreover, exponential stability and the rapid stabilization of solutions are obtained by energy and...