Upper semicontinuity of the attractor for a nonlinear hyperbolic-parabolic coupled system with fractional Laplacian
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913232782884864 |
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| author | Santos, Manoel J. Dos Lobato, Renato F. C. |
| author_facet | Santos, Manoel J. Dos Lobato, Renato F. C. |
| contents | In this paper we establish the existence and uniqueness of global solutions (in time), as well as the existence, regularity and stability (upper semicontinuity) of the attractor for the semigroup generated by the solutions of a two-dimensional nonlinear hyperbolic-parabolic coupled system with fractional Laplacian. In addition, we also obtain the existence of an exponential attractor and show that this attractor has a finite fractal dimension in a space containing the phase space of the dynamical system. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_08954 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Upper semicontinuity of the attractor for a nonlinear hyperbolic-parabolic coupled system with fractional Laplacian Santos, Manoel J. Dos Lobato, Renato F. C. Dynamical Systems 35B40, 35B41, 37L30 In this paper we establish the existence and uniqueness of global solutions (in time), as well as the existence, regularity and stability (upper semicontinuity) of the attractor for the semigroup generated by the solutions of a two-dimensional nonlinear hyperbolic-parabolic coupled system with fractional Laplacian. In addition, we also obtain the existence of an exponential attractor and show that this attractor has a finite fractal dimension in a space containing the phase space of the dynamical system. |
| title | Upper semicontinuity of the attractor for a nonlinear hyperbolic-parabolic coupled system with fractional Laplacian |
| topic | Dynamical Systems 35B40, 35B41, 37L30 |
| url | https://arxiv.org/abs/2308.08954 |