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Properties of the Global Attractors for the Variable Parameter Diffusion Equation with Fading Memory

Author: ZhaoJuanXia
Tutor: WangZuo
School: Northwest Normal University
Course: Basic mathematics
Keywords: Nonclassical diffusion equations Global attractors Upper semi-continuity Critical exponent Fractal dimension Fading memory
CLC: O19
Type: Master's thesis
Year: 2013
Downloads: 21
Quote: 0
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Abstract


In this article, we mainly studied the non-classical diffusion equation with fading memory. The specific study of two questions:i) We study the initial value problems of the non-classical diffusion equation with variable parameters and fading memory: where a≥0. By using semi-group theory, we obtain the continuity of solutions in the weak topological space, when the nonlinearity is critical and the forcing term only belongs to H-1(Q). Therefore, upper semi-continuity of the global attractors for the variable parameter diffusion equation with fading memory is obtained. The results are the improvements and extensions of the results of paper.ii) We study the following a periodic boundary value problem for a non-classical diffusion equation with memory: where uo(x, t)is a known periodic function in x∈R3for t≤0, and we assume L=(L1,L2,L3). By using semi-group theory and fractal dimension theory, we obtain the fractal dimension of the global attractor is finite when the nonlinearity is critical and the forcing term only belongs to C2(R,R). The results are the improvements and extensions of the results of paper.

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CLC: > Mathematical sciences and chemical > Mathematics > Dynamical systems theory
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