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LIMITING BEHAVIOR OF TRAJECTORY ATTRACTORS OF PERTURBED REACTION-DIFFUSION EQUATIONS

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Affiliation of Author(s):理学院
Journal:DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Key Words:Reaction-diffusion equations perturbation trajectory attractor global attractor convergence fractal dimension
Abstract:In this paper, we study the relations between the long-time dynamical behavior of the perturbed reaction-diffusion equations and the exact reaction-diffusion equations with concave and convex nonlinear terms and prove that bounded sets of solutions of the perturbed reaction-diffusion equations converges to the trajectory attractor u(0) of the exact reaction-diffusion equations when t -> infinity and epsilon -> 0(+). In particular, we show that the trajectory attractor u(epsilon) of the perturbed reaction-diffusion equations converges to the trajectory attractor u(0) of the exact reaction-diffusion equations when epsilon -> 0(+). Moreover, we derive the upper and lower bounds of the fractal dimension for the global attractor of the perturbed reaction-diffusion equations.
ISSN No.:1531-3492
Translation or Not:no
Date of Publication:2019-10-01
Correspondence Author:ygc
Date of Publication:2019-10-01