Singularly perturbed partly dissipative reaction-diffusion systems in case of exchange of stabilities
- Butuzov, Valentin F.
- Nefedov, Nikolai N.
- Schneider, Klaus R.
2010 Mathematics Subject Classification
- 35B25 35K57
- Initial boundary value problem, singularly perturbed partly dissipative reaction-diffusion system, exchange of stabilities, asymptotic lower and upper solutions
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.