Existence of solutions to a nonlinear fractional diffusion equation with exponential growth
In this paper, we study a Cauchy problem for a space–time fractional diffusion equation with exponential nonlinearity. Based on the standard Lp-Lq estimates of strongly continuous semigroup generated by fractional Laplace operator, we investigate the existence of global solutions for initial data w...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2024-01-01
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| Series: | Nonlinear Analysis |
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| Online Access: | https://www.journals.vu.lt/nonlinear-analysis/article/view/34228 |
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| _version_ | 1849686664296792064 |
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| author | Jia Wei He Yong Zhou Ahmed Alsaedi Bashir Ahmad |
| author_facet | Jia Wei He Yong Zhou Ahmed Alsaedi Bashir Ahmad |
| author_sort | Jia Wei He |
| collection | DOAJ |
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In this paper, we study a Cauchy problem for a space–time fractional diffusion equation with exponential nonlinearity. Based on the standard Lp-Lq estimates of strongly continuous semigroup generated by fractional Laplace operator, we investigate the existence of global solutions for initial data with small norm in Orlicz space exp Lp(Rd) and a time weighted Lr(Rd) space. In the framework of the Hölder interpolation inequality, we also discuss the existence of local solutions without the Orlicz space.
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| format | Article |
| id | doaj-art-b9f692e545f64b6e8a58cef35174a659 |
| institution | DOAJ |
| issn | 1392-5113 2335-8963 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj-art-b9f692e545f64b6e8a58cef35174a6592025-08-20T03:22:38ZengVilnius University PressNonlinear Analysis1392-51132335-89632024-01-0129210.15388/2024.29.34228Existence of solutions to a nonlinear fractional diffusion equation with exponential growthJia Wei He0https://orcid.org/0000-0001-5283-585XYong Zhou1Ahmed Alsaedi2Bashir Ahmad3https://orcid.org/0000-0001-5350-2977Guangxi UniversityXiangtan UniversityKing Abdulaziz UniversityKing Abdulaziz University In this paper, we study a Cauchy problem for a space–time fractional diffusion equation with exponential nonlinearity. Based on the standard Lp-Lq estimates of strongly continuous semigroup generated by fractional Laplace operator, we investigate the existence of global solutions for initial data with small norm in Orlicz space exp Lp(Rd) and a time weighted Lr(Rd) space. In the framework of the Hölder interpolation inequality, we also discuss the existence of local solutions without the Orlicz space. https://www.journals.vu.lt/nonlinear-analysis/article/view/34228diffusion equationCaputo’s fractional derivativeexponential growthOrlicz spaces |
| spellingShingle | Jia Wei He Yong Zhou Ahmed Alsaedi Bashir Ahmad Existence of solutions to a nonlinear fractional diffusion equation with exponential growth Nonlinear Analysis diffusion equation Caputo’s fractional derivative exponential growth Orlicz spaces |
| title | Existence of solutions to a nonlinear fractional diffusion equation with exponential growth |
| title_full | Existence of solutions to a nonlinear fractional diffusion equation with exponential growth |
| title_fullStr | Existence of solutions to a nonlinear fractional diffusion equation with exponential growth |
| title_full_unstemmed | Existence of solutions to a nonlinear fractional diffusion equation with exponential growth |
| title_short | Existence of solutions to a nonlinear fractional diffusion equation with exponential growth |
| title_sort | existence of solutions to a nonlinear fractional diffusion equation with exponential growth |
| topic | diffusion equation Caputo’s fractional derivative exponential growth Orlicz spaces |
| url | https://www.journals.vu.lt/nonlinear-analysis/article/view/34228 |
| work_keys_str_mv | AT jiaweihe existenceofsolutionstoanonlinearfractionaldiffusionequationwithexponentialgrowth AT yongzhou existenceofsolutionstoanonlinearfractionaldiffusionequationwithexponentialgrowth AT ahmedalsaedi existenceofsolutionstoanonlinearfractionaldiffusionequationwithexponentialgrowth AT bashirahmad existenceofsolutionstoanonlinearfractionaldiffusionequationwithexponentialgrowth |