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
Abstract:
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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