WIAS Preprint No. 572, (2000)

Singularly perturbed partly dissipative reaction-diffusion systems in case of exchange of stabilities


Authors

  • Butuzov, Valentin F.
  • Nefedov, Nikolai N.
  • Schneider, Klaus R.

2010 Mathematics Subject Classification

  • 35B25 35K57

Keywords

  • Initial boundary value problem, singularly perturbed partly dissipative reaction-diffusion system, exchange of stabilities, asymptotic lower and upper solutions

DOI

10.20347/WIAS.PREPRINT.572

Abstract

We consider the singularly perturbed partly dissipative reaction-diffusion system ε2 (∂u ⁄ ∂t - ∂2u ⁄ ∂x2 = g(u,v,x,t,ε), ∂v ⁄ ∂t = ƒ(u,v,x,t,ε) under the condition that the degenerate equation g(u,v,t,0) = 0 has two solutions u = φi(v,x,t), i = 1,2, that intersect (exchange of stabilities). Our main result concerns existence and asymptotic behavior in ε of the solution of the initial boundary value problem under consideration. The proof is based on the method of asymptotic lower and upper solutions.

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