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Global existence and non-existence for the degenerate and uniformly parabolic equations with gradient term

Published online by Cambridge University Press:  22 May 2013

Haifeng Shang
Haifeng Shang*
Affiliation:
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, People's Republic of China ([email protected])
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Abstract

We study the Cauchy problem for the degenerate and uniformly parabolic equations with gradient term. The local existence, global existence and non-existence of solutions are obtained. In the case of global solvability, we get the exact estimates of a solution. In particular, we obtain the global existence of solutions in the limiting case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 3 , June 2013 , pp. 643 - 668
Copyright
Copyright © Royal Society of Edinburgh 2013 

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