Identification problems for semilinear integro-differential hyperbolic equations with transformed arguments
Articolo
Data di Pubblicazione:
2011
Citazione:
Identification problems for semilinear integro-differential hyperbolic equations with transformed arguments / A. Lorenzi, F. Messina. - In: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS. - ISSN 0928-0219. - 19:1(2011 May), pp. 49-81. [10.1515/JIIP.2011.023]
Abstract:
The aim of the present paper is to generalize the results in [Denisov, J. Inverse Ill-Posed Probl. 16: 837–848, 2008.] devoted to a one-dimensional semilinear wave equation and consisting of recovering a time-dependent function α representing the transformed argument. More exactly: (i) we will deal with a general semilinear integro-differential hyperbolic d-dimensional equation in divergence form (d = 1, 2, 3); (ii) the space-time set considered here is a smooth cylinder where surface boundary conditions are prescribed; (iii) the term with transformed arguments is allowed to contain integral operators; (iv) the additional information is of integral type.
The existence and uniqueness results for our specific problem are deduced as consequences of similar results for an operator integro-differential identification problem in a Hilbert space.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
existence and uniqueness results; semigroup theory; Semilinear integro-differential hyperbolic equations; unknown transformed arguments
Elenco autori:
A. Lorenzi, F. Messina
Link alla scheda completa: