Attractors of the ReactionDiffusion Equations 

Author  KangYaHu 
Tutor  MaQiaoZhen 
School  Northwest Normal University 
Course  Applied Mathematics 
Keywords  Reactiondifusion equation measure of noncompactness pullback condition (C) squeezing property pullback attractors exponentialattractors 
CLC  O19 
Type  Master's thesis 
Year  2013 
Downloads  2 
Quotes  0 
In this master dissertation, we study the longtime behavior of the reactiondifusion 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 reactiondifusion 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 reactiondifusion 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）∈ L_{b}^{R, L2（Ω）} which is translation bounded but not translation compact, i.e.,Finally, we study the existence of exponential attractor for the nonlinearreactiondifusion equation with the distribution derivative termwhere is a bounded smooth domain in R^{n}. f^{i}, f∈L^{2}（Ω）（i=1,2,..., n）,is the distribution derivative.