EXISTENCE OF THE WEAK SOLUTION FOR A STRATIFIED DIFFUSION MODEL VIA AN ITERATIVE METHOD
We study the existence and uniqueness of the solution of a non-linear stratified diffusion problem. To this aim, we construct an alternative method based on successive substitutions of a linear approximation of the original problem. We use the theory of partial differential equations and mathematica...
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| Format: | Article |
| Language: | English |
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Universidad de Costa Rica
2018-02-01
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| Series: | Revista de Matemática: Teoría y Aplicaciones |
| Subjects: | |
| Online Access: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/32235 |
| _version_ | 1797761760447430656 |
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| author | RICARDO CANO MACÍAS JORGE MAURICIO RUIZ V. |
| author_facet | RICARDO CANO MACÍAS JORGE MAURICIO RUIZ V. |
| author_sort | RICARDO CANO MACÍAS |
| collection | DOAJ |
| description | We study the existence and uniqueness of the solution of a non-linear stratified diffusion problem. To this aim, we construct an alternative method based on successive substitutions of a linear approximation of the original problem. We use the theory of partial differential equations and
mathematical induction to prove that each of the linear problems of the iteration has a unique weak solution. Finally, we prove that the sequence of weak solutions obtained is a Cauchy sequence that converges to the weak solution of the problem. |
| first_indexed | 2024-03-12T19:17:42Z |
| format | Article |
| id | doaj.art-255bc6d04bea4d33b669110e3d231a6b |
| institution | Directory Open Access Journal |
| issn | 2215-3373 |
| language | English |
| last_indexed | 2024-03-12T19:17:42Z |
| publishDate | 2018-02-01 |
| publisher | Universidad de Costa Rica |
| record_format | Article |
| series | Revista de Matemática: Teoría y Aplicaciones |
| spelling | doaj.art-255bc6d04bea4d33b669110e3d231a6b2023-08-02T05:23:01ZengUniversidad de Costa RicaRevista de Matemática: Teoría y Aplicaciones2215-33732018-02-0125115116810.15517/rmta.v1i25.3223527172EXISTENCE OF THE WEAK SOLUTION FOR A STRATIFIED DIFFUSION MODEL VIA AN ITERATIVE METHODRICARDO CANO MACÍAS0JORGE MAURICIO RUIZ V.1Facultad de Ingeniería, Universidad de La Sabana, Chía, Colombia.Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá D.C., Colombia.We study the existence and uniqueness of the solution of a non-linear stratified diffusion problem. To this aim, we construct an alternative method based on successive substitutions of a linear approximation of the original problem. We use the theory of partial differential equations and mathematical induction to prove that each of the linear problems of the iteration has a unique weak solution. Finally, we prove that the sequence of weak solutions obtained is a Cauchy sequence that converges to the weak solution of the problem.https://revistas.ucr.ac.cr/index.php/matematica/article/view/32235solución débilmétodo iterativodifusión no lineal |
| spellingShingle | RICARDO CANO MACÍAS JORGE MAURICIO RUIZ V. EXISTENCE OF THE WEAK SOLUTION FOR A STRATIFIED DIFFUSION MODEL VIA AN ITERATIVE METHOD Revista de Matemática: Teoría y Aplicaciones solución débil método iterativo difusión no lineal |
| title | EXISTENCE OF THE WEAK SOLUTION FOR A STRATIFIED DIFFUSION MODEL VIA AN ITERATIVE METHOD |
| title_full | EXISTENCE OF THE WEAK SOLUTION FOR A STRATIFIED DIFFUSION MODEL VIA AN ITERATIVE METHOD |
| title_fullStr | EXISTENCE OF THE WEAK SOLUTION FOR A STRATIFIED DIFFUSION MODEL VIA AN ITERATIVE METHOD |
| title_full_unstemmed | EXISTENCE OF THE WEAK SOLUTION FOR A STRATIFIED DIFFUSION MODEL VIA AN ITERATIVE METHOD |
| title_short | EXISTENCE OF THE WEAK SOLUTION FOR A STRATIFIED DIFFUSION MODEL VIA AN ITERATIVE METHOD |
| title_sort | existence of the weak solution for a stratified diffusion model via an iterative method |
| topic | solución débil método iterativo difusión no lineal |
| url | https://revistas.ucr.ac.cr/index.php/matematica/article/view/32235 |
| work_keys_str_mv | AT ricardocanomacias existenceoftheweaksolutionforastratifieddiffusionmodelviaaniterativemethod AT jorgemauricioruizv existenceoftheweaksolutionforastratifieddiffusionmodelviaaniterativemethod |