Trajectory attractor for a system of two reaction-diffusion equations with diffusion coefficient delta(t) -> 0+as t -> plus a

摘要

The method of trajectory attractors (see [1–6]) makes it possible to effectively study the limit behavior of solutions to partial differential equations for which the theory of global attractors (see [7, 8]) is not directly applicable, for example, due to nonunique solvability of the corresponding Cauchy problem. In the present paper, we construct the trajectory attractor for a nonautonomous reactiondiffusion system where one equation has a timedependent diffusion coefficient that tends to zero as t→+∞. In [9, 10], an analogous problem has been studied for autonomous reactiondiffusion systems having one timeindependent diffusion coefficient that approaches zero as a parameter of the problem.