论文标题:反应扩散方程和退化抛物方程的整体吸引子和距离估计
Attractors and Distance Estimates of Reaction-diffusion Systems and Degenerate Parabolic Equation
论文作者 胡晓红
论文导师 张兴友,论文学位 硕士,论文专业 应用数学
论文单位 重庆大学,点击次数 113,论文页数 58页File Size1159k
2004-04-20论文网 http://www.lw23.com/lunwen_601327152/ 整体吸引子,均匀化,反应扩散方程,先验估计,退化和抛物方程,殆周期函数,Diophantine条件,散度形式
global attractor, homogenization, reaction-diffusion systems,prior estimates, degenerate parabolic equations, almost-periodic functions, Diophantine condition, divergence form
这篇论文一方面深入地研究了一类反应扩散问题的整体吸引子A~ε和相应均匀化方程的整体吸引子A~0，并给出了A~ε和A~0的距离估计，另一方面研究了一类退化的抛物问题的整体吸引子A~ε和相应均匀化方程的整体吸引子A~0，并给出了A~ε和A~0在给定空间的距离估计。 本文主要利用先验估计得出了下列问题的整体吸引子和距离估计：其中第一个方程所得的结果推广了B.Fiedler，M.L Vishik，M.fendiev和S.Zelik已有的结论。第二个方程的结果是对退化抛物方程的进一步研究。
On one hand, the global attractor A of a reaction-diffusion systems and the homogenized attractor A0 of the corresponding homogenized equation respectively are studied, and the explicit estimate for the distance between A and A0 is also studied. On the other hand, the global attractor A of a degenerate parabolic equation and the homogenized attractor A0 of the corresponding homogenized equation respectively are studied, and the explicit estimate for the distance between A and A0 is also studied for a given space.Using prior estimates, we obtain above results for the following non-degenerate and degenerate parabolic problems: The results of the first equations extend the known results existing in the literature of B. Fiedler, M.L Vishik, M.fendiev and S.Zelik, and the second equation extends the known results existing in the degenerate parabolic equation.
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