Por favor, use este identificador para citar o enlazar este ítem:
http://cimat.repositorioinstitucional.mx/jspui/handle/1008/1063| THE MONGE-AMPERE EQUATION AND THE NEWTON PROBLEM OF MINIMAL RESISTANCE | |
| Alejandro Mendez Rojas | |
| Acceso Abierto | |
| Atribución-NoComercial | |
| Resistencia mínima | |
| The Monge-Ampere (M-A) equation in an important fully nonlinear elliptic equation. Its study is motivated from problems in different areas of knowledge, one of such, is shape optimization. In particular, the Newton problem of optimal aerodynamical profiles, Buttazzo (2009). Consequently, the purpose of this thesis is to present the M-A equation in a multidisciplinary process. First, we introduce the problem of minimal resistance. The underlying model is based, essentially, on the same assumptions that Newton made. It is shown that the problem corresponds to the minimization of a functional. The variational analysis of the problem is carried out. Noteworthy, in subdomains where the solution is smooth, the M-A equation must be satisfied as a necessary condition of optimality. The notion of solutions of the M-A is a delicate issue. An analysis is presented following Gutierrez (2016). For applications, the numerical solution of the M-A equation is of great interest. We show a mesh free approach as in Bohmer & Schaback (2019). | |
| 01-09-2020 | |
| Trabajo de grado, maestría | |
| OTRAS | |
| Versión aceptada | |
| acceptedVersion - Versión aceptada | |
| Aparece en las colecciones: | Tesis del CIMAT |
Cargar archivos:
| Fichero | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| TE 774.pdf | 662.18 kB | Adobe PDF | Visualizar/Abrir |