Direct and inverse abstract Cauchy problems with fractional powers of almost sectorial operators
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914350478917632 |
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| author | Restrepo, Joel E. |
| author_facet | Restrepo, Joel E. |
| contents | We derive the explicit solution operator of an abstract Cauchy problem involving a time-variable coefficient and a fractional power of an almost sectorial operator. The time-variable coefficient is recovered by solving the inverse abstract Cauchy problem using the solution operator representation. As a complement, we also study similar problems by considering almost sectorial operators that depend on a time-variable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Direct and inverse abstract Cauchy problems with fractional powers of almost sectorial operators Restrepo, Joel E. Analysis of PDEs 65J08, 65N21, 34K08, 47A05 We derive the explicit solution operator of an abstract Cauchy problem involving a time-variable coefficient and a fractional power of an almost sectorial operator. The time-variable coefficient is recovered by solving the inverse abstract Cauchy problem using the solution operator representation. As a complement, we also study similar problems by considering almost sectorial operators that depend on a time-variable. |
| title | Direct and inverse abstract Cauchy problems with fractional powers of almost sectorial operators |
| topic | Analysis of PDEs 65J08, 65N21, 34K08, 47A05 |
| url | https://arxiv.org/abs/2408.00240 |