Well-Posedness and Regularity Results for Fractional Wave Equations with Time-Dependent Coefficients
Fractional wave equations with time-dependent coefficients are natural generations of classical wave equations which can be used to characterize propagation of wave in inhomogeneous media with frequency-dependent power-law behavior. This paper discusses the well-posedness and regularity results of t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/11/644 |
| _version_ | 1797468229513248768 |
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| author | Li Peng Yong Zhou |
| author_facet | Li Peng Yong Zhou |
| author_sort | Li Peng |
| collection | DOAJ |
| description | Fractional wave equations with time-dependent coefficients are natural generations of classical wave equations which can be used to characterize propagation of wave in inhomogeneous media with frequency-dependent power-law behavior. This paper discusses the well-posedness and regularity results of the weak solution for a fractional wave equation allowing that the coefficients may have low regularity. Our analysis relies on mollification arguments, Galerkin methods, and energy arguments. |
| first_indexed | 2024-03-09T19:03:28Z |
| format | Article |
| id | doaj.art-5dd7022001eb4a86820a6e59695699b6 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T19:03:28Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-5dd7022001eb4a86820a6e59695699b62023-11-24T04:45:22ZengMDPI AGFractal and Fractional2504-31102022-11-0161164410.3390/fractalfract6110644Well-Posedness and Regularity Results for Fractional Wave Equations with Time-Dependent CoefficientsLi Peng0Yong Zhou1Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, ChinaFaculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, ChinaFractional wave equations with time-dependent coefficients are natural generations of classical wave equations which can be used to characterize propagation of wave in inhomogeneous media with frequency-dependent power-law behavior. This paper discusses the well-posedness and regularity results of the weak solution for a fractional wave equation allowing that the coefficients may have low regularity. Our analysis relies on mollification arguments, Galerkin methods, and energy arguments.https://www.mdpi.com/2504-3110/6/11/644fractional wave equationsenergy estimatewell-posednessregularity |
| spellingShingle | Li Peng Yong Zhou Well-Posedness and Regularity Results for Fractional Wave Equations with Time-Dependent Coefficients Fractal and Fractional fractional wave equations energy estimate well-posedness regularity |
| title | Well-Posedness and Regularity Results for Fractional Wave Equations with Time-Dependent Coefficients |
| title_full | Well-Posedness and Regularity Results for Fractional Wave Equations with Time-Dependent Coefficients |
| title_fullStr | Well-Posedness and Regularity Results for Fractional Wave Equations with Time-Dependent Coefficients |
| title_full_unstemmed | Well-Posedness and Regularity Results for Fractional Wave Equations with Time-Dependent Coefficients |
| title_short | Well-Posedness and Regularity Results for Fractional Wave Equations with Time-Dependent Coefficients |
| title_sort | well posedness and regularity results for fractional wave equations with time dependent coefficients |
| topic | fractional wave equations energy estimate well-posedness regularity |
| url | https://www.mdpi.com/2504-3110/6/11/644 |
| work_keys_str_mv | AT lipeng wellposednessandregularityresultsforfractionalwaveequationswithtimedependentcoefficients AT yongzhou wellposednessandregularityresultsforfractionalwaveequationswithtimedependentcoefficients |