Zhang Guo-chu. Stability of Stationary State Solution for a Reaction Density-Dependent Diffusion Equation[J]. Applied Mathematics and Mechanics, 1989, 10(11): 987-996.
Citation: Zhang Guo-chu. Stability of Stationary State Solution for a Reaction Density-Dependent Diffusion Equation[J]. Applied Mathematics and Mechanics, 1989, 10(11): 987-996.

Stability of Stationary State Solution for a Reaction Density-Dependent Diffusion Equation

  • Received Date: 1988-11-29
  • Publish Date: 1989-11-15
  • 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 φ(u) and φ(u) 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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