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Evolution inclusions governed by subdifferentials in reflexive Banach spaces
| Content Provider | Semantic Scholar |
|---|---|
| Author | Akagi, Goro Otani, Mitsuharu |
| Copyright Year | 2004 |
| Abstract | Abstract.The existence, uniqueness and regularity of strong solutions for Cauchy problem and periodic problem are studied for the evolution equation: % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaadw % hacaGGOaGaamiDaiaacMcacaGGVaGaamizaiaadshacqGHRaWkcqGH % ciITcqaHvpGAcaGGOaGaamyDaiaacIcacaWG0bGaaiykaiaacMcacq % GHniYjcaWGMbGaaiikaiaadshacaGGPaGaaiilaiaaykW7caWG0bGa % eyicI4SaaiyxaiaaicdacaGGSaGaaGPaVlaadsfacaGGBbGaaiilaa % aa!5486! $$du(t)/dt + \partial \varphi (u(t)) \mathrel\backepsilon f(t),\,t \in ]0,\,T[,$$ where ∂φ is the so-called subdifferential operator from a real Banach space V into its dual V*. The study in the Hilbert space setting (V = V* = H: Hilbert space) is already developed in detail so far. However, the study here is done in the V−V* setting which is not yet fully pursued. Our method of proof relies on approximation arguments in a Hilbert space H. To assure this procedure, it is assumed that the embeddings % MathType!Translator!2!1!AMS LaTeX.tdl!TeX -- AMS-LaTeX! % MathType!MTEF!2!1!+- % feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaiabgk % OimlaadIeacqGHckcZcaWGwbWaaWbaaSqabeaacaGGQaaaaaaa!3D44! $$V \subset H \subset V^* $$ are both dense and continuous. |
| Starting Page | 519 |
| Ending Page | 541 |
| Page Count | 23 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00028-004-0162-y |
| Volume Number | 4 |
| Alternate Webpage(s) | https://page-one.springer.com/pdf/preview/10.1007/s00028-004-0162-y |
| Alternate Webpage(s) | https://doi.org/10.1007/s00028-004-0162-y |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
