Regular Solutions of First-Order Hamilton–Jacobi Equations for Boundary Control Problems and Applications to Economics |
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Authors: | Silvia Faggian |
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Institution: | (1) Dipartimento di Matematica, Universita di Pisa, Via F. Buonarroti 2, I-56127 Pisa, Italy |
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Abstract: | This is the first of two papers
regarding a family of linear convex control problems in Hilbert
spaces and the related Hamilton–Jacobi–Bellman equations. The
framework is motivated by an application to boundary control of
a PDE modeling investments with vintage capital. Existence and
uniqueness of a strong solution (namely, the limit of classic
solutions of approximating equations, introduced by Barbu and Da
Prato) is investigated. Moreover, such a solution is proved to be
C1 in the space variable. |
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Keywords: | Linear convex control Boundary
control Hamilton– Jacobi– Bellman equations |
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