Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GLOBAL ATTRACTOR FOR A CLASS OF QUASILINEAR DEGENERATE PARABOLIC EQUATIONS WITH NONLINEARITY OF ARBITRARY ORDER

  • Received : 2019.09.23
  • Accepted : 2021.02.09
  • Published : 2021.07.31
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Abstract

In this paper we study the existence and long-time behavior of weak solutions to a class of quasilinear degenerate parabolic equations involving weighted p-Laplacian operators with a new class of nonlinearities. First, we prove the existence and uniqueness of weak solutions by combining the compactness and monotone methods and the weak convergence techniques in Orlicz spaces. Then, we prove the existence of global attractors by using the asymptotic a priori estimates method.

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Acknowledgement

The authors would like to thank the reviewers for their helpful comments and suggestions, which help us to improve the presentation of the paper. We also thank the anonymous reviewer for suggesting an interesting problem, which will be our future research subject. The research of the third author is supported by the Hung Vuong University.

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