Well-posedness and spectral properties of heat and wave equations with non-local conditions |
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Authors: | Delio Mugnolo Serge Nicaise |
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Affiliation: | 1. Institut für Analysis, Universität Ulm, 89069 Ulm, Germany;2. Université de Valenciennes et du Hainaut Cambrésis, LAMAV, FR CNRS 2956, ISTV, F-59313 Valenciennes Cedex 9, France |
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Abstract: | We consider the one-dimensional heat and wave equations but – instead of boundary conditions – we impose on the solution certain non-local, integral constraints. An appropriate Hilbert setting leads to an integration-by-parts formula in Sobolev spaces of negative order and eventually allows us to use semigroup theory leading to analytic well-posedness, hence sharpening regularity results previously obtained by other authors. In doing so we introduce a parametrization of such integral conditions that includes known cases but also shows the connection with more usual boundary conditions, like periodic ones. In the self-adjoint case, we even obtain eigenvalue asymptotics of so-called Weyl?s type. |
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Keywords: | 47D06 35J20 34B10 |
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