Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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GLOBAL ATTRACTORS FOR NONLOCAL PARABOLIC EQUATIONS WITH A NEW CLASS OF NONLINEARITIES

  • Anh, Cung The (Department of Mathematics Hanoi National University of Education) ;
  • Tinh, Le Tran (Department of Mathematics Hong Duc University) ;
  • Toi, Vu Manh (Faculty of Computer Science and Engineering Thuyloi University)
  • Received : 2017.04.06
  • Accepted : 2017.12.15
  • Published : 2018.05.01
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Abstract

In this paper we consider a class of nonlocal parabolic equations in bounded domains with Dirichlet boundary conditions and a new class of nonlinearities. We first prove the existence and uniqueness of weak solutions by using the compactness method. Then we study the existence and fractal dimension estimates of the global attractor for the continuous semigroup generated by the problem. We also prove the existence of stationary solutions and give a sufficient condition for the uniqueness and global exponential stability of the stationary solution. The main novelty of the obtained results is that no restriction is imposed on the upper growth of the nonlinearities.

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References

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