Global Existence, Asymptotic Behavior and Uniform Attractors for a Third Order in Time Dynamics

CAO Jie

doi:10.13371/j.cnki.chin.q.j.m.2016.03.001

Chinese Quarterly Journal of Mathematics >

2016 , Vol. 31 >Issue 3: 221 - 236

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.03.001

Global Existence, Asymptotic Behavior and Uniform Attractors for a Third Order in Time Dynamics

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College of Information Science and Technology,Donghua University

CAO Jie(1990-), male, native of Zhengzhou, Henan, a PhD candidate of Donghua University, engages in nonlinear evolution equations and in¯nite-dimensional dynamical systems.

Received date: 2016-01-20

Online published: 2020-11-04

Supported by

Supported by the National Natural Science Foundation of China(11271066)； Supported by the Shanghai Education Commission(13ZZ048)；

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Abstract

In this paper,a third order（in time） partial differential equation in Rⁿ is considered.By using semigroup method and constructing Lyapunov function,we establish the global existence,asymptotic behavior and uniform attractors in nonhomogeneous case.In addition,we also obtain the results of well-posedness in semilinear case.

Key words： third order in time dynamics; well-posedness; asymptotic behavior; uniform attractors

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CAO Jie . Global Existence, Asymptotic Behavior and Uniform Attractors for a Third Order in Time Dynamics[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(3) : 221 -236 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.03.001

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