Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator
In this article, we mainly study the qualitative properties of solutions for dual fractional-order parabolic equations with nonlocal Monge-Ampère operators in different domains ∂tβμ(y,t)−Dατμ(y,t)=f(μ(y,t)).{\partial }_{t}^{\beta }\mu \left(y,t)-{D}_{\alpha }^{\tau }\mu \left(y,t)=f\left(\mu \left(y...
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De Gruyter
2025-06-01
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| Series: | Advances in Nonlinear Analysis |
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| Online Access: | https://doi.org/10.1515/anona-2025-0086 |
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| author | Yang Zerong He Yong |
| author_facet | Yang Zerong He Yong |
| author_sort | Yang Zerong |
| collection | DOAJ |
| description | In this article, we mainly study the qualitative properties of solutions for dual fractional-order parabolic equations with nonlocal Monge-Ampère operators in different domains ∂tβμ(y,t)−Dατμ(y,t)=f(μ(y,t)).{\partial }_{t}^{\beta }\mu \left(y,t)-{D}_{\alpha }^{\tau }\mu \left(y,t)=f\left(\mu \left(y,t)). We first establish a series of maximum principles and averaging effects theorems for antisymmetric functions and then used the method of moving planes and sliding planes to establish radial symmetry, monotonicity, nonexistence, and Liouville theorem for positive solutions. |
| format | Article |
| id | doaj-art-9fc6bf63bb334aa28efa1c1ce8c05ef7 |
| institution | Matheson Library |
| issn | 2191-950X |
| language | English |
| publishDate | 2025-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj-art-9fc6bf63bb334aa28efa1c1ce8c05ef72025-06-30T06:54:28ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2025-06-01141442510.1515/anona-2025-0086Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operatorYang Zerong0He Yong1School of Mathematics and Statistics Science, Hainan University, Haikou, 570228, Hainan, ChinaSchool of Mathematics and Statistics Science, Hainan University, Haikou, 570228, Hainan, ChinaIn this article, we mainly study the qualitative properties of solutions for dual fractional-order parabolic equations with nonlocal Monge-Ampère operators in different domains ∂tβμ(y,t)−Dατμ(y,t)=f(μ(y,t)).{\partial }_{t}^{\beta }\mu \left(y,t)-{D}_{\alpha }^{\tau }\mu \left(y,t)=f\left(\mu \left(y,t)). We first establish a series of maximum principles and averaging effects theorems for antisymmetric functions and then used the method of moving planes and sliding planes to establish radial symmetry, monotonicity, nonexistence, and Liouville theorem for positive solutions.https://doi.org/10.1515/anona-2025-0086dual parabolic equationsmonotonicityradial symmetrynonexistenceliouville theorem35r1135b5035b0626a3347g3035b53 |
| spellingShingle | Yang Zerong He Yong Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator Advances in Nonlinear Analysis dual parabolic equations monotonicity radial symmetry nonexistence liouville theorem 35r11 35b50 35b06 26a33 47g30 35b53 |
| title | Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator |
| title_full | Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator |
| title_fullStr | Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator |
| title_full_unstemmed | Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator |
| title_short | Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator |
| title_sort | qualitative properties of solutions for dual fractional parabolic equations involving nonlocal monge ampere operator |
| topic | dual parabolic equations monotonicity radial symmetry nonexistence liouville theorem 35r11 35b50 35b06 26a33 47g30 35b53 |
| url | https://doi.org/10.1515/anona-2025-0086 |
| work_keys_str_mv | AT yangzerong qualitativepropertiesofsolutionsfordualfractionalparabolicequationsinvolvingnonlocalmongeampereoperator AT heyong qualitativepropertiesofsolutionsfordualfractionalparabolicequationsinvolvingnonlocalmongeampereoperator |