Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domains
This paper deals with the asymptotic behavior of solutions to non-autonomous, fractional, stochastic p-Laplacian equations driven by additive white noise and random terms defined on the unbounded domain ℝN. We first prove the existence and uniqueness of solutions for polynomial drift terms of arbitr...
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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2021-12-01
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| Series: | Bulletin of Mathematical Sciences |
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| Online Access: | http://www.worldscientific.com/doi/epdf/10.1142/S1664360720500204 |
| _version_ | 1818871714246819840 |
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| author | Renhai Wang Bixiang Wang |
| author_facet | Renhai Wang Bixiang Wang |
| author_sort | Renhai Wang |
| collection | DOAJ |
| description | This paper deals with the asymptotic behavior of solutions to non-autonomous, fractional, stochastic p-Laplacian equations driven by additive white noise and random terms defined on the unbounded domain ℝN. We first prove the existence and uniqueness of solutions for polynomial drift terms of arbitrary order. We then establish the existence and uniqueness of pullback random attractors for the system in L2(ℝN). This attractor is further proved to be a bi-spatial (L2(ℝN),Lr(ℝN))-attractor for any r ∈ [2,∞), which is compact, measurable in Lr(ℝN) and attracts all random subsets of L2(ℝN) with respect to the norm of Lr(ℝN). Finally, we show the robustness of these attractors as the intensity of noise and the random coefficients approach zero. The idea of uniform tail-estimates as well as the method of higher-order estimates on difference of solutions are employed to derive the pullback asymptotic compactness of solutions in Lr(ℝN) for r ∈ [2,∞) in order to overcome the non-compactness of Sobolev embeddings on ℝN and the nonlinearity of the fractional p-Laplace operator. |
| first_indexed | 2024-12-19T12:27:18Z |
| format | Article |
| id | doaj.art-12b7eeaf609d48ec84e5b33cc55d64dc |
| institution | Directory Open Access Journal |
| issn | 1664-3607 1664-3615 |
| language | English |
| last_indexed | 2024-12-19T12:27:18Z |
| publishDate | 2021-12-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | Bulletin of Mathematical Sciences |
| spelling | doaj.art-12b7eeaf609d48ec84e5b33cc55d64dc2022-12-21T20:21:32ZengWorld Scientific PublishingBulletin of Mathematical Sciences1664-36071664-36152021-12-011132050020-12050020-5010.1142/S166436072050020410.1142/S1664360720500204Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domainsRenhai Wang0Bixiang Wang1School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P. R. ChinaDepartment of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USAThis paper deals with the asymptotic behavior of solutions to non-autonomous, fractional, stochastic p-Laplacian equations driven by additive white noise and random terms defined on the unbounded domain ℝN. We first prove the existence and uniqueness of solutions for polynomial drift terms of arbitrary order. We then establish the existence and uniqueness of pullback random attractors for the system in L2(ℝN). This attractor is further proved to be a bi-spatial (L2(ℝN),Lr(ℝN))-attractor for any r ∈ [2,∞), which is compact, measurable in Lr(ℝN) and attracts all random subsets of L2(ℝN) with respect to the norm of Lr(ℝN). Finally, we show the robustness of these attractors as the intensity of noise and the random coefficients approach zero. The idea of uniform tail-estimates as well as the method of higher-order estimates on difference of solutions are employed to derive the pullback asymptotic compactness of solutions in Lr(ℝN) for r ∈ [2,∞) in order to overcome the non-compactness of Sobolev embeddings on ℝN and the nonlinearity of the fractional p-Laplace operator.http://www.worldscientific.com/doi/epdf/10.1142/S1664360720500204fractional p-laplacian equationbi-spatial random attractoradditive noiserobustnessunbounded domain |
| spellingShingle | Renhai Wang Bixiang Wang Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domains Bulletin of Mathematical Sciences fractional p-laplacian equation bi-spatial random attractor additive noise robustness unbounded domain |
| title | Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domains |
| title_full | Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domains |
| title_fullStr | Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domains |
| title_full_unstemmed | Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domains |
| title_short | Asymptotic behavior of non-autonomous fractional p-Laplacian equations driven by additive noise on unbounded domains |
| title_sort | asymptotic behavior of non autonomous fractional p laplacian equations driven by additive noise on unbounded domains |
| topic | fractional p-laplacian equation bi-spatial random attractor additive noise robustness unbounded domain |
| url | http://www.worldscientific.com/doi/epdf/10.1142/S1664360720500204 |
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