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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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참고문헌 (30)
참고문헌 신청
A. S. Ackleh / 2000 / Existence-uniqueness and long time behavior for a class of nonlocal nonlinear parabolic evolution equations / Proc. Amer. Math. Soc. 128(12):3483~3492
R. M. P. Almeida / 2016 / On a nonlocal degenerate parabolic problem / Nonlinear Anal. Real World Appl. 27:146~157
R. M. P. Almeida / 2016 / A reaction-diffusion model for the non-local coupled system: existence, uniqueness, long-time behaviour and localization properties of solutions / IMA J. Appl. Math. 81(2):344~364
M. Anguiano / 2010 / Asymptotic behaviour of nonlocal reaction-diffusion equations / Nonlinear Anal. 73(9):3044~3057
C. T. Anh / 2014 / Global attractor for a semilinear strongly degenerate parabolic equation on ${\mathbb{R}}^N$ / NoDEA Nonlinear Differential Equations Appl. 21(5):663~678
R. M. P. Almeida / 2016 / On a nonlocal degenerate parabolic problem / Nonlinear Anal. Real World Appl. 27:146~157
R. M. P. Almeida / 2016 / A reaction-diffusion model for the non-local coupled system: existence, uniqueness, long-time behaviour and localization properties of solutions / IMA J. Appl. Math. 81(2):344~364
M. Anguiano / 2010 / Asymptotic behaviour of nonlocal reaction-diffusion equations / Nonlinear Anal. 73(9):3044~3057
C. T. Anh / 2014 / Global attractor for a semilinear strongly degenerate parabolic equation on
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