数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (3): 1167-1180.doi: 10.1016/S0252-9602(12)60089-7

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GLOBAL EXISTENCE AND Lp ESTIMATES FOR SOLUTIONS OF DAMPED WAVE EQUATION WITH NONLINEAR CONVECTION IN#br# MULTI-DIMENSIONAL SPACE

陈娇   

  1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
  • 收稿日期:2010-10-29 修回日期:2011-04-04 出版日期:2012-05-20 发布日期:2012-05-20
  • 基金资助:

    The author is supported by Shanghai Municipal Natural Science Foundation 09ZR1413500 and National Natural Science Foundation of China 11071162.

GLOBAL EXISTENCE AND Lp ESTIMATES FOR SOLUTIONS OF DAMPED WAVE EQUATION WITH NONLINEAR CONVECTION IN#br# MULTI-DIMENSIONAL SPACE

 CHEN Jiao   

  1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2010-10-29 Revised:2011-04-04 Online:2012-05-20 Published:2012-05-20
  • Supported by:

    The author is supported by Shanghai Municipal Natural Science Foundation 09ZR1413500 and National Natural Science Foundation of China 11071162.

摘要:

In this article, the author studies the Cauchy problem of the damped wave equation with a nonlinear convection term in multi-dimensions. The author shows that a classical solution to the Cauchy problem exists globally in time under smallness condition on the initial perturbation. Furthermore, the author obtains the Lp (2≤ p ≤ ∞) decay estimates of the solution.

关键词: Damped wave equation with nonlinear convection, frequency decomposition method, Greens function, energy method, global existence

Abstract:

In this article, the author studies the Cauchy problem of the damped wave equation with a nonlinear convection term in multi-dimensions. The author shows that a classical solution to the Cauchy problem exists globally in time under smallness condition on the initial perturbation. Furthermore, the author obtains the Lp (2≤ p ≤ ∞) decay estimates of the solution.

Key words: Damped wave equation with nonlinear convection, frequency decomposition method, Greens function, energy method, global existence

中图分类号: 

  • 35L70