DECAY RATE FOR DEGENERATE CONVECTION DIFFUSION EQUATIONS IN BOTH ONE AND SEVERAL SPACE DIMENSIONS

doi:10.1016/S0252-9602(15)60001-7

Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (2): 281-302.doi: 10.1016/S0252-9602(15)60001-7

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DECAY RATE FOR DEGENERATE CONVECTION DIFFUSION EQUATIONS IN BOTH ONE AND SEVERAL SPACE DIMENSIONS

Yunguang LU¹, Christian KLINGENBERG², Ujjwal KOLEY², Xuezhou LU³

1. Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China;
2. Institut für Mathematik, Julius-Maximilians-Universität Würzburg, Germany;
3. Laboratoire Ondes and Milieux Complexes UMR 6294, CNRS-Université|du Havre, France

Received:2013-12-24 Revised:2014-01-08 Online:2015-03-20 Published:2015-03-20
Contact: Xuezhou LU Laboratoire Ondes and Milieux Complexes UMR 6294, CNRS-Université du Havre, France E-mail: xuezhou.lu@gmail.com E-mail:xuezhou.lu@gmail.com
Supported by:
This work was partially supported by the Natural Science Foundation of China (11271105), a grant from the China Scholarship Council and a Humboldt fellowship of Germany.

Abstract

Abstract:

We consider degenerate convection-diffusion equations in both one space dimension and several space dimensions. In the first part of this article, we are concerned with the decay rate of solutions of one dimension convection diffusion equation. On the other hand, in the second part of this article, we are concerned with a decay rate of derivatives of solution of convection diffusion equation in several space dimensions.

Key words: Degenerate convection-diffusion equations, regularity, decay rate, Lax-Oleinik type inequality

CLC Number:

35B50

Yunguang LU, Christian KLINGENBERG, Ujjwal KOLEY, Xuezhou LU. DECAY RATE FOR DEGENERATE CONVECTION DIFFUSION EQUATIONS IN BOTH ONE AND SEVERAL SPACE DIMENSIONS[J].Acta mathematica scientia,Series B, 2015, 35(2): 281-302.

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DECAY RATE FOR DEGENERATE CONVECTION DIFFUSION EQUATIONS IN BOTH ONE AND SEVERAL SPACE DIMENSIONS

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