Global Well-Posedness and Analyticity of Generalized Porous Medium Equation in Fourier-Besov-Morrey Spaces with Variable Exponent
In this paper, we consider the generalized porous medium equation. For small initial data <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>u</mi><mn>0</mn></msub></seman...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/5/498 |
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| author | Muhammad Zainul Abidin Jiecheng Chen |
| author_facet | Muhammad Zainul Abidin Jiecheng Chen |
| author_sort | Muhammad Zainul Abidin |
| collection | DOAJ |
| description | In this paper, we consider the generalized porous medium equation. For small initial data <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>u</mi><mn>0</mn></msub></semantics></math></inline-formula> belonging to the Fourier-Besov-Morrey spaces with variable exponent, we obtain the global well-posedness results of generalized porous medium equation by using the Fourier localization principle and the Littlewood-Paley decomposition technique. Furthermore, we also show Gevrey class regularity of the solution. |
| first_indexed | 2024-03-09T06:08:42Z |
| format | Article |
| id | doaj.art-b67f3db02fa042dfa1b9f3d03d12f2fc |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T06:08:42Z |
| publishDate | 2021-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b67f3db02fa042dfa1b9f3d03d12f2fc2023-12-03T12:01:14ZengMDPI AGMathematics2227-73902021-02-019549810.3390/math9050498Global Well-Posedness and Analyticity of Generalized Porous Medium Equation in Fourier-Besov-Morrey Spaces with Variable ExponentMuhammad Zainul Abidin0Jiecheng Chen1College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaCollege of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaIn this paper, we consider the generalized porous medium equation. For small initial data <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>u</mi><mn>0</mn></msub></semantics></math></inline-formula> belonging to the Fourier-Besov-Morrey spaces with variable exponent, we obtain the global well-posedness results of generalized porous medium equation by using the Fourier localization principle and the Littlewood-Paley decomposition technique. Furthermore, we also show Gevrey class regularity of the solution.https://www.mdpi.com/2227-7390/9/5/498global well-posednessanalyticityporous medium equationFourier-Besov-Morrey space with variable exponent |
| spellingShingle | Muhammad Zainul Abidin Jiecheng Chen Global Well-Posedness and Analyticity of Generalized Porous Medium Equation in Fourier-Besov-Morrey Spaces with Variable Exponent Mathematics global well-posedness analyticity porous medium equation Fourier-Besov-Morrey space with variable exponent |
| title | Global Well-Posedness and Analyticity of Generalized Porous Medium Equation in Fourier-Besov-Morrey Spaces with Variable Exponent |
| title_full | Global Well-Posedness and Analyticity of Generalized Porous Medium Equation in Fourier-Besov-Morrey Spaces with Variable Exponent |
| title_fullStr | Global Well-Posedness and Analyticity of Generalized Porous Medium Equation in Fourier-Besov-Morrey Spaces with Variable Exponent |
| title_full_unstemmed | Global Well-Posedness and Analyticity of Generalized Porous Medium Equation in Fourier-Besov-Morrey Spaces with Variable Exponent |
| title_short | Global Well-Posedness and Analyticity of Generalized Porous Medium Equation in Fourier-Besov-Morrey Spaces with Variable Exponent |
| title_sort | global well posedness and analyticity of generalized porous medium equation in fourier besov morrey spaces with variable exponent |
| topic | global well-posedness analyticity porous medium equation Fourier-Besov-Morrey space with variable exponent |
| url | https://www.mdpi.com/2227-7390/9/5/498 |
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