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Solutions in the large for certain nonlinear parabolic equations and applications*

Published online by Cambridge University Press:  14 November 2011

Huijiang Zhao  and
Changjiang Zhu
Huijiang Zhao
Affiliation:
Young Scientist Laboratory of Mathematical Physics, Institute of Mathematical Sciences, Chinese Academy of Sciences, P.O. Box 71007, Wuhan 430071, People's Republic of China
Changjiang Zhu
Affiliation:
Young Scientist Laboratory of Mathematical Physics, Institute of Mathematical Sciences, Chinese Academy of Sciences, P.O. Box 71007, Wuhan 430071, People's Republic of China
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Abstract

We prove some results on the global existence of smooth solutions for certain nonlinear parabolic systems of the form Ut + A(U)Ux = DUxx. Here U is a vector and A(U), D are matrices with D a constant, positive matrix. We show how to use our results to study the global continuous (or generalised) solutions to the corresponding nonlinear hyperbolic conservation laws and a conjecture is given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 1 , 1996 , pp. 19 - 45
Copyright
Copyright © Royal Society of Edinburgh 1996

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