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 [8] to the case in which the nonlinearities might be less smooth. Namely we show that Gateaux shape derivatives exists when the no...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-09-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/221/abstr.html |
| _version_ | 1828426098681053184 |
|---|---|
| author | David Gomez-Castro |
| author_facet | David Gomez-Castro |
| author_sort | David Gomez-Castro |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T16:39:27Z |
| format | Article |
| id | doaj.art-d20d335f37ea488f86bcd6fa9f38052b |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T16:39:27Z |
| publishDate | 2017-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-d20d335f37ea488f86bcd6fa9f38052b2022-12-22T01:41:16ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-09-012017221,111Shape differentiation of steady-state reaction-diffusion problems arising in chemical engineering with non-smooth kinetics with dead coreDavid Gomez-Castro0 Univ. Complutense de Madrid, Spain 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.http://ejde.math.txstate.edu/Volumes/2017/221/abstr.htmlShape differentiationreaction-diffusionchemical engineeringdead core |
| spellingShingle | David Gomez-Castro Shape differentiation of steady-state reaction-diffusion problems arising in chemical engineering with non-smooth kinetics with dead core Electronic Journal of Differential Equations Shape differentiation reaction-diffusion chemical engineering dead core |
| title | Shape differentiation of steady-state reaction-diffusion problems arising in chemical engineering with non-smooth kinetics with dead core |
| title_full | Shape differentiation of steady-state reaction-diffusion problems arising in chemical engineering with non-smooth kinetics with dead core |
| title_fullStr | Shape differentiation of steady-state reaction-diffusion problems arising in chemical engineering with non-smooth kinetics with dead core |
| title_full_unstemmed | Shape differentiation of steady-state reaction-diffusion problems arising in chemical engineering with non-smooth kinetics with dead core |
| title_short | Shape differentiation of steady-state reaction-diffusion problems arising in chemical engineering with non-smooth kinetics with dead core |
| title_sort | shape differentiation of steady state reaction diffusion problems arising in chemical engineering with non smooth kinetics with dead core |
| topic | Shape differentiation reaction-diffusion chemical engineering dead core |
| url | http://ejde.math.txstate.edu/Volumes/2017/221/abstr.html |
| work_keys_str_mv | AT davidgomezcastro shapedifferentiationofsteadystatereactiondiffusionproblemsarisinginchemicalengineeringwithnonsmoothkineticswithdeadcore |