Fréchet differentiability of solution mappings for semilinear second order evolution equations |
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| Authors: | Junhong Ha Shin-ichi Nakagiri Hiroki Tanabe |
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| Affiliation: | a School of Liberal Arts, Korea University of Technology and Education, Republic of Korea
b Department of Applied Mathematics, Faculty of Engineering, Kobe University, Japan |
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| Abstract: | In this paper we establish the strong Fréchet differentiability of maps from the set of initial values and forcing terms into the set of solutions for semilinear second order evolution equations. Also, under the weaker conditions of nonlinear terms we establish the strong Gâteaux differentiability of the solution maps. An application of results to semilinear strongly damped wave equations is given. |
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| Keywords: | Second order evolution equations Fré chet differentiability Gâ teaux differentiability Semilinear damped wave equations |
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