Shape differentiation of steady-state reaction-diffusion problems arising in chemical engineering with non-smooth kinetics with dead core
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...
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| Format: | Journal article |
| Language: | English |
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Department of Mathematics, Texas State University
2017
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| Summary: | 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. |
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