What is it about?
The paper developed a new framework on how to describe the long-time behavior the solutions of partial differential equations. A finiteness property of strongly uniformly approximating as well as a strong equicontinuity is obtained.
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Why is it important?
A important feature of some classes of dissipative systems is that they possess a finite dimensional structure, or the systems are in essence of finite degrees, even the phase spaces in general are infinite dimension. Hence, it arrives at the notion of a global attractor. Here we present new insights and introduce a notion of a strongly compact strong trajectory attractor.
Perspectives
Global attractors are ever anticipated to be very complicated objects (fractals), which obstruct their applications. We expect that our finite strong uniform tracking property and strong equicontinuity, which are now described by the existence of a strongly compact strong trajectory attractor, will do some good for their practical utilization, for instance for numerical simulations.
Songsong Lu
Read the Original
This page is a summary of: Strongly compact strong trajectory attractors for evolutionary systems and their applications, Asymptotic Analysis, May 2023, IOS Press,
DOI: 10.3233/asy-221805.
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