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Existence and stability of solutions with periodically moving weak internal layers |
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| Authors: | VF Butuzov |
| Institution: | a Department of Physics, Moscow State University, Vorob'jovy Gory, 119899 Moscow, Russia b Humboldt University of Berlin, Institute of Mathematics, Rudower Chaussee 25, 12489 Berlin, Germany c Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany |
| Abstract: | We consider the periodic parabolic differential equation  under the assumption that ε is a small positive parameter and that the degenerate equation f(u,x,t,0)=0 has two intersecting solutions. We derive conditions such that there exists an asymptotically stable solution up(x,t,ε) which is T-periodic in t, satisfies no-flux boundary conditions and tends to the stable composed root of the degenerate equation as ε→0. |
| Keywords: | Singularly perturbed reaction diffusion equation Periodic boundary value problem Boundary layers |
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