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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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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Abstract 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.
AbstractList 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.
Abstract 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.
ArticleNumber 22
Author Jiang, Yan Zhuo
Sun, Cong
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10.1109/TAC.2012.2209260
10.1016/j.automatica.2005.04.006
10.1016/j.jfa.2013.03.010
10.1007/BF02790212
10.1016/j.jmaa.2020.124538
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10.3934/dcds.2002.8.399
10.1016/j.automatica.2015.01.024
10.1007/s10440-017-0106-5
10.1016/j.jde.2015.01.038
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Snippet 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...
Abstract This paper deals with the existence and stability of the solution for a class heat equation with logarithmic nonlinearity. Using the potential well...
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SubjectTerms 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
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Title Existence and stability of a one-dimensional heat equation with logarithmic nonlinearity
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