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- W4313443050 abstract "This paper is concerned with the analytical and numerical dissipativity of the space-fractional Allen–Cahn equation, a generalization of the classic Allen–Cahn equation by replacing the local Laplacian with a nonlocal fractional Laplacian. It is first proved that the continuous dynamical system is dissipative as its local counterpart in Hα and Lq, q=2k+2 for k≥0, spaces. Then it is shown that the backward Euler method preserves the dissipativity of the underlying system, that is, the discrete-in-time dynamical system with time-step parameter τ is still dissipative in Hα and Lq spaces. The existence of the global attractor for both continuous and discrete dynamical systems are then obtained. A numerical example is given to confirm the theoretical results." @default.
- W4313443050 created "2023-01-06" @default.
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- W4313443050 date "2023-05-01" @default.
- W4313443050 modified "2023-09-29" @default.
- W4313443050 title "Analytical and numerical dissipativity for the space-fractional Allen–Cahn equation" @default.
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- W4313443050 doi "https://doi.org/10.1016/j.matcom.2022.12.012" @default.
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