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Attractors of Non-autonomous Reaction Diffusion Equations in Unbounded Domains

Author: DengJianBing
Tutor: XieYongQin
School: Changsha University of Science and Technology
Course: Applied Mathematics
Keywords: Reaction-diffusion equation Unbounded Domain Asymptotic a priori estimate Asymptotically tight Uniform attractor
CLC: O175
Type: Master's thesis
Year: 2010
Downloads: 23
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Abstract


In this master thesis, we mainly consider the following non- autonomous on unbounded domains reaction-diffusion equations which the long time behavior of the nonlinear term f satisfies the polynomial growth condition , g ∈ Lb2 (R, L2 (Rn)) there is merely a translation tight circles instead of panning function classes on the theoretical framework , in the second chapter we give non- uniform attractor autonomous system of basic concepts and structures , and on this basis to establish consistency in unbounded domains attractor existence theorem of general discrimination . in order to further characterize the structure of the uniform attractor , we will have the strength bounded domain concept extended to a continuous process on unbounded domains , the corresponding strength of a continuous process , and the establishment of uniform attractor corresponding discriminant theorem of existence . in order to verify the non- autonomous system (Ⅰ) on unbounded domains in the process of cluster compactness necessary , in Chapter gives a particularly suitable validation process evolution equations induced asymptotic tight asymptotic first new methods that posteriori estimation as a specific application , in the fourth chapter , on with supercritical nonlinearity of non-autonomous reaction-diffusion equation , for external items are not panning tight situation , we first prove its corresponding process family tight uniform attractor critical condition - process clusters in (L2 (Rn), L2 (Rn)) and (L2 (Rn), Lp (Rn)) in the asymptotic compactness . then use the third chapter gives an abstract theorem consistent existence of attractors .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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