Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (6): 2051-2063.doi: 10.1016/S0252-9602(10)60190-7

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NONLINEAR EVOLUTION SYSTEMS AND GREEN'S FUNCTION

 WANG Wei-Ke   

  1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2010-09-06 Online:2010-11-20 Published:2010-11-20
  • Supported by:

    The authors are supported by National Science Foundation of China (11071162) and Shanghai Municipal Natural Science Foundation (09ZR1413500).

Abstract:

In this paper, we will introduce how to apply Green's function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative  structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen's principle. Then, for other nonlinear
dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green's function of the linearized system and micro-local analysis, such as frequency decomposition and so on.

Key words: conservation laws with dissipative structure, pointwise estimate,  Greens function, generalized Huygens principle

CLC Number: 

  • 35L65
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