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Large-time behaviour of solutions to non-Newtonian filtration equations with nonlinear boundary sources

Published online by Cambridge University Press:  04 August 2010

Zejia Wang ,
Jingxue Yin  and
Chunpeng Wang
Zejia Wang
Affiliation:
Department of Mathematics, Jilin University, Changchun 130012, People's Republic of China (wangcp@jlu.edu.cn)
Jingxue Yin
Affiliation:
Department of Mathematics, Jilin University, Changchun 130012, People's Republic of China (wangcp@jlu.edu.cn)
Chunpeng Wang
Affiliation:
Department of Mathematics, Jilin University, Changchun 130012, People's Republic of China (wangcp@jlu.edu.cn)
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Abstract

This paper deals with the large-time behaviour of solutions to the exterior problem of the non-Newtonian filtration equation with first-order term and nonlinear boundary source. In particular, the critical global exponent and the critical Fujita exponent are determined or estimated. An interesting phenomenon is shown: there exists a threshold value for the coefficient of the first-order term such that the critical global exponent is strictly less than the critical Fujita exponent when the coefficient is under this threshold, while these two exponents are identically equal when the coefficient is over this value.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 4 , August 2010 , pp. 833 - 855
Copyright
Copyright © Royal Society of Edinburgh 2010

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