Boundedness of Global Solutions for a Heat Equation with Exponential Gradient Source

Joint Authors

Li, Yanyan
Zhang, Zhengce

Source

Abstract and Applied Analysis

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

Mathematics

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