Boundedness of Global Solutions for a Heat Equation with Exponential Gradient Source
Joint Authors
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-12-27
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We consider a one-dimensional semilinear parabolic equation with exponential gradient source and provide a complete classification of large time behavior of the classical solutions: either the space derivative of the solution blows up in finite time with the solution itself remaining bounded or the solution is global and converges in C1 norm to the unique steady state.
The main difficulty is to prove C1 boundedness of all global solutions.
To do so, we explicitly compute a nontrivial Lyapunov's functional by carrying out the method of Zelenyak.
American Psychological Association (APA)
Zhang, Zhengce& Li, Yanyan. 2011. Boundedness of Global Solutions for a Heat Equation with Exponential Gradient Source. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-10.
https://search.emarefa.net/detail/BIM-468976
Modern Language Association (MLA)
Zhang, Zhengce& Li, Yanyan. Boundedness of Global Solutions for a Heat Equation with Exponential Gradient Source. Abstract and Applied Analysis No. 2012 (2012), pp.1-10.
https://search.emarefa.net/detail/BIM-468976
American Medical Association (AMA)
Zhang, Zhengce& Li, Yanyan. Boundedness of Global Solutions for a Heat Equation with Exponential Gradient Source. Abstract and Applied Analysis. 2011. Vol. 2012, no. 2012, pp.1-10.
https://search.emarefa.net/detail/BIM-468976
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-468976