Electron. J. Differential Equations, Vol. 2017 (2017), No. 221, pp. 1-11.

Shape differentiation of steady-state reaction-diffusion problems arising in chemical engineering with non-smooth kinetics with dead core

David Gomez-Castro

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 [8] 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
email: dgcastro@ucm.es

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