Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equation
Abstract The linear stabilization problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) is considered when the spatial variable lies in [0,1] $[0,1]$. First, the existence and uniqueness of global solutions are proved. Next, the exponential stability of the equation is esta...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-10-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2387-7 |
| _version_ | 1819226079014944768 |
|---|---|
| author | Nejib Smaoui Boumediène Chentouf Ala’ Alalabi |
| author_facet | Nejib Smaoui Boumediène Chentouf Ala’ Alalabi |
| author_sort | Nejib Smaoui |
| collection | DOAJ |
| description | Abstract The linear stabilization problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) is considered when the spatial variable lies in [0,1] $[0,1]$. First, the existence and uniqueness of global solutions are proved. Next, the exponential stability of the equation is established in L2(0,1) $L^{2} (0,1)$. Then, a linear adaptive boundary control is put forward. Finally, numerical simulations for both non-adaptive and adaptive problems are provided to illustrate the analytical outcomes. |
| first_indexed | 2024-12-23T10:19:47Z |
| format | Article |
| id | doaj.art-f8273f932dbc4a1a81aa32eca8517743 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-23T10:19:47Z |
| publishDate | 2019-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-f8273f932dbc4a1a81aa32eca85177432022-12-21T17:50:43ZengSpringerOpenAdvances in Difference Equations1687-18472019-10-012019111710.1186/s13662-019-2387-7Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equationNejib Smaoui0Boumediène Chentouf1Ala’ Alalabi2Department of Mathematics, Faculty of Science, Kuwait UniversityDepartment of Mathematics, Faculty of Science, Kuwait UniversityDepartment of Mathematics, Faculty of Science, Kuwait UniversityAbstract The linear stabilization problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) is considered when the spatial variable lies in [0,1] $[0,1]$. First, the existence and uniqueness of global solutions are proved. Next, the exponential stability of the equation is established in L2(0,1) $L^{2} (0,1)$. Then, a linear adaptive boundary control is put forward. Finally, numerical simulations for both non-adaptive and adaptive problems are provided to illustrate the analytical outcomes.http://link.springer.com/article/10.1186/s13662-019-2387-7Modified generalized Korteweg–de Vries–Burgers equationWell-posednessExponential stabilityBoundary control |
| spellingShingle | Nejib Smaoui Boumediène Chentouf Ala’ Alalabi Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equation Advances in Difference Equations Modified generalized Korteweg–de Vries–Burgers equation Well-posedness Exponential stability Boundary control |
| title | Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equation |
| title_full | Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equation |
| title_fullStr | Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equation |
| title_full_unstemmed | Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equation |
| title_short | Boundary linear stabilization of the modified generalized Korteweg–de Vries–Burgers equation |
| title_sort | boundary linear stabilization of the modified generalized korteweg de vries burgers equation |
| topic | Modified generalized Korteweg–de Vries–Burgers equation Well-posedness Exponential stability Boundary control |
| url | http://link.springer.com/article/10.1186/s13662-019-2387-7 |
| work_keys_str_mv | AT nejibsmaoui boundarylinearstabilizationofthemodifiedgeneralizedkortewegdevriesburgersequation AT boumedienechentouf boundarylinearstabilizationofthemodifiedgeneralizedkortewegdevriesburgersequation AT alaalalabi boundarylinearstabilizationofthemodifiedgeneralizedkortewegdevriesburgersequation |