Frechet differentiability of the solutions of a semilinear abstract Cauchy problem

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:307

Article

Herdman, T ; Spies, R

关键词: abstract Cauchy problem;    analytic semigroup;    infinitesimal generator;    Frechet differentiability;    Frechet derivative;   

DOI  :  10.1016/j.jmaa.2005.02.044

来源: Elsevier

【 摘 要 】

Sufficient conditions are found under which the solutions z(t; q) of a serailinear abstract Cauchy problem of the form d/dt z(t) = A(q)z(t) + F (q, t, z (t)) are Frechet differentiable with respect to the parameter q. An explicit form is provided for the sensitivity equation satisfied by the Frechet derivative D(q)z(t; q). (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

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