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Existence and decay rates of smooth solutions for a non-uniformly parabolic equation

Published online by Cambridge University Press:  12 July 2007

Jinghua Wang
Affiliation:
Institute of System Sciences, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People's Republic of China (jwang@amss.iss.ac.cn)
Hui Zhang
Affiliation:
Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 1001871, People's Republic of China (huizhang@math.pku.edu.cn)

Abstract

We obtain the existence and decay rates of the classical solution to the initial-value problem of a non-uniformly parabolic equation. Our method is to set up two equivalent sequences of the successive approximations. One converges to a weak solution of the initial-value problem; the other shows that the weak solution is the classical solution for t > 0. Moreover, we show how bounds of the derivatives to the classical solution depend explicitly on the interval with compact support in (0, ∞). Then we study decay rates of this classical solution.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2002

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