Applied Mathematics and Mechanics (English Edition) ›› 1989, Vol. 10 ›› Issue (11): 1039-1049.

• 论文 • 上一篇    下一篇

STABILITY OF STATIONARY STATE SOLUTION FOR A REACTION DENSITY-DEPENDENT DIFFUSION EQUATION

张国初   

  1. Beijing Institute of Economics, Beijing
  • 收稿日期:1988-11-29 出版日期:1989-11-18 发布日期:1989-11-18

STABILITY OF STATIONARY STATE SOLUTION FOR A REACTION DENSITY-DEPENDENT DIFFUSION EQUATION

Zhang Guo-chu   

  1. Beijing Institute of Economics, Beijing
  • Received:1988-11-29 Online:1989-11-18 Published:1989-11-18

摘要: In this paper we are interested in the large time behavior of the nonlinear diffusion equation u1=(φ(u))xx+φ(u), (x∈R, f∈R+=(0,+∞)) We consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u= 0 or u=1 is unstable under some assumptions, etc.

Abstract: In this paper we are interested in the large time behavior of the nonlinear diffusion equation u1=(φ(u))xx+φ(u), (x∈R, f∈R+=(0,+∞)) We consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u= 0 or u=1 is unstable under some assumptions, etc.

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