Chinese Quarterly Journal of Mathematics ›› 2016, Vol. 31 ›› Issue (3): 221-236.doi: 10.13371/j.cnki.chin.q.j.m.2016.03.001

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

  

  1. College of Information Science and Technology,Donghua University
  • Received:2016-01-20 Online:2016-09-30 Published:2020-11-04
  • About author: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.
  • Supported by:
    Supported by the National Natural Science Foundation of China(11271066); Supported by the Shanghai Education Commission(13ZZ048);

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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