Fréchet differentiability of the solutions of a semilinear abstract Cauchy problem

Terry Herdman,Ruben Spies

doi:10.1016/j.jmaa.2005.02.044

Fréchet differentiability of the solutions of a semilinear abstract Cauchy problem

Terry Herdman, Ruben Spies

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https://doi.org/10.1016/j.jmaa.2005.02.044

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Journal: Journal of Mathematical Analysis and Applications	Publication Date: Mar 30, 2005
Citations: 4	License type: cc-by-nc-sa

Affiliation: Virginia Tech

#Semilinear Problem #Solutions Of Cauchy Problem + Show 7 more

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Abstract

Sufficient conditions are found under which the solutions z ( t ; q ) of a semilinear abstract Cauchy problem of the form d d t z ( t ) = A ( q ) z ( t ) + F ( q , t , z ( t ) ) are Fréchet differentiable with respect to the parameter q. An explicit form is provided for the sensitivity equation satisfied by the Fréchet derivative D q z ( t ; q ) .

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