Attractors of the Reaction-Diffusion Equations
|School||Northwest Normal University|
|Keywords||Reaction-difusion equation measure of noncompactness pullback condition (C) squeezing property pullback attractors exponentialattractors|
In this master dissertation, we study the long-time behavior of the reaction-difusion equations based on the theory of measure of noncompactness and socalled the condition （C）, which appears in fluid mechanics, solid mechanicsand heat conduction theory, see for instance [1,3,7,22,23].Firstly, we obtain the existence of pullback attractor of the reaction-difusion equationwhere is a bounded smooth domain inRn, f is a C1function and the externalforcing term g（x, t）∈L22loc（R, L（）） only satisfy the integration conditionSecondly, we prove the existence of exponential attractor of the reaction-difusion equation where is a bounded smooth domain inRn, f is a Lipschitz function satisfyingthe polynomial growth of arbitrary order and the external forcing term g（x, t）∈ LbR, L2（Ω） which is translation bounded but not translation compact, i.e.,Finally, we study the existence of exponential attractor for the nonlinearreaction-difusion equation with the distribution derivative termwhere is a bounded smooth domain in Rn. fi, f∈L2（Ω）（i=1,2,..., n）,is the distribution derivative.