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Fréchet differentiability of the solutions of a semilinear abstract Cauchy problem |
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| Authors: | Terry Herdman Ruben Spies |
| Institution: | a Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA b Instituto de Matemática Aplicada del Litoral, IMAL-CONICET, Güemes 3450, Argentina c Departamento de Matemática, Facultad de Ingeniería Química, Universidad Nacional del Litoral, Santiago del Estero 2829, C.P. 3000 Santa Fe, Argentina |
| Abstract: | Sufficient conditions are found under which the solutions z(t;q) of a semilinear abstract Cauchy problem of the form  are Fréchet differentiable with respect to the parameter q. An explicit form is provided for the sensitivity equation satisfied by the Fréchet derivative Dqz(t;q). |
| Keywords: | Abstract Cauchy problem Analytic semigroup Infinitesimal generator Fré chet differentiability Fré chet derivative |
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