KERNEL SECTIONS OF MULTI-VALUED PROCESSES WITH APPLICATION TO THE NONLINEAR REACTION-DIFFUSION EQUATIONS IN UNBOUNDED DOMAINS
KERNEL SECTIONS OF MULTI-VALUED PROCESSES WITH APPLICATION TO THE NONLINEAR REACTION-DIFFUSION EQUATIONS IN UNBOUNDED DOMAINS
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DOI：
10.1090/s0033-569x-09-01150-0
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发表时间：
2009-03
影响因子：
0.8
通讯作者：
Yejuan Wang;Shengfan Zhou
中科院分区：
文献类型：
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作者：
Yejuan Wang;Shengfan Zhou
首先，我们引入多值过程的回调欧米伽极限紧致性的概念，作为自治和非自治框架中类似概念的扩展。接下来，我们提出无限维多值过程的非空局部有界核（核部分都是紧致的、不变的和回拉吸引的）存在的必要和充分条件（回拉耗散性和回拉欧米伽极限紧致性）。此外，我们证明了在点耗散性和均匀欧米伽极限紧致性的一般假设下，确保一系列多值过程的膨胀核部分存在均匀吸引子和均匀前向吸引的结果。最后，我们用无界域中的非线性反应扩散模型来说明抽象理论。
First, we introduce the concept of pullback omega-limit compactness for multivalued processes, as an extension of the similar concept in the autonomous and nonautonomous framework. Next, we present the necessary and sufficient, conditions (pullback dissipativeness and pullback omega-limit compactness) for the existence of a nonempty local bounded kernel (kernel sections are all compact, invariant and pullback attracting) of an infinite dimensional multi-valued process. In addition, we prove a result ensuring the existence of a uniform attractor and the uniform forward attraction of the inflated kernel sections of a family of multi-valued processes under the general assumptions of point dissipativeness and uniform omega-limit compactness. Finally, we illustrate the abstract theory with a nonlinear reaction-diffusion model in an unbounded domain.