Linear first-order evolution problems without initial conditions. (English) Zbl 1205.35027
Summary: Direct and inverse problems for first-order in time linear evolution problems without initial conditions, i.e. related to the unbounded time-intervals \((-\infty , 0]\) and \(\mathbb{R}\), are considered in the framework of Banach spaces. Some degenerate in time problems related to a bounded time-interval are also considered. The approach for solving the previous problems is related to both \(C_{0}\)-and Analytic Semigroup Theory. The inverse problem consists of recovering an unknown element in the Banach space entering the source term.
MSC:
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35R30 | Inverse problems for PDEs |
| 34G10 | Linear differential equations in abstract spaces |
| 45K05 | Integro-partial differential equations |
| 45M10 | Stability theory for integral equations |
| 47D06 | One-parameter semigroups and linear evolution equations |
Keywords:
Fourier problem; problem without initial conditions; linear \(C_{0}\)- and analytic semigroups; direct and inverse problemsReferences:
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