Stabilization of solutions to a FitzHugh-Nagumo type system
نویسندگان
چکیده
We consider a bistable reaction-diffusion system arising in the theory of phase transitions; it appears in several physical contexts such as thin magnetic films and the microphase separation in diblock copolymer melts. Mathematically it takes the form of an Allen-Cahn equation coupled to an elliptic equation. This system possesses a Lyapunov functional which represents the Gibbs free energy of the phase separation problem. We study the large time behavior of the solution orbits, and use the fact that the problem has a gradient structure to prove their stabilization by means of a version of Łojasiewicz inequality. keywords: gradient flow, Łojasiewicz inequality, stabilization of solutions, FitzHugh-Nagumo system, diblock copolymer, infinite dimensional dynamical systems
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