In this paper we consider an extension of the results in shape differentiation of semilinear equations with smooth nonlinearity presented by Diaz and Gomez-Castro  to the case in which the nonlinearities might be less smooth. Namely we show that Gateaux shape derivatives exists when the nonlinearity is only Lipschitz continuous, and we will give a definition of the derivative when the nonlinearity has a blow up. In this direction, we study the case of root-type nonlinearities.
Submitted July 20, 2017. Published September 16, 2017.
Math Subject Classifications: 35J61, 46G05, 35B30.
Key Words: Shape differentiation; reaction-diffusion; chemical engineering; dead core.
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| David Gómez-Castro |
Instituto de Matemática Interdisciplinar
Universidad Complutense de Madrid
Plaza de las Ciencias 3
28040 Madrid, Spain
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