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

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...

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Bibliographic Details
Published inJournal of inequalities and applications Vol. 2025; no. 1; pp. 22 - 14
Main Authors Sun, Cong, Jiang, Yan Zhuo
Format Journal Article
LanguageEnglish
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
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Summary: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 backstepping methods.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-025-03269-8