Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Dynamical systems theory

Attractors of the Reaction-Diffusion Equations

Author KangYaHu
Tutor MaQiaoZhen
School Northwest Normal University
Course Applied Mathematics
Keywords Reaction-difusion equation measure of noncompactness pullback condition (C) squeezing property pullback attractors exponentialattractors
CLC O19
Type Master's thesis
Year 2013
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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.

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