A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient
We study the backward problem with time-dependent coefficient which is a severely ill-posed problem. We regularize this problem by combining quasi-boundary value method and quasi-reversibility method and then obtain sharp error estimate between the exact solution and the regularized solution. A nume...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/943621 |
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| _version_ | 1849410097907761152 |
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| author | Pham Hoang Quan Le Minh Triet Dang Duc Trong |
| author_facet | Pham Hoang Quan Le Minh Triet Dang Duc Trong |
| author_sort | Pham Hoang Quan |
| collection | DOAJ |
| description | We study the backward problem with time-dependent coefficient which is a severely ill-posed problem. We regularize this problem by combining quasi-boundary value method and quasi-reversibility method and then obtain sharp error estimate between the exact solution and the regularized solution. A numerical experiment is given in order to illustrate our results. |
| format | Article |
| id | doaj-art-76decd8afefb4f8ebb4cc324cbc785ea |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-76decd8afefb4f8ebb4cc324cbc785ea2025-08-20T03:35:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/943621943621A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent CoefficientPham Hoang Quan0Le Minh Triet1Dang Duc Trong2Department of Mathematics and Applications, Sai Gon University, 273 An Duong Vuong, District 5, Ho Chi Minh City, VietnamDepartment of Mathematics and Applications, Sai Gon University, 273 An Duong Vuong, District 5, Ho Chi Minh City, VietnamDepartment of Mathematics, University of Natural Science, Vietnam National University, 227 Nguyen Van Cu, District 5, Ho Chi Minh City, VietnamWe study the backward problem with time-dependent coefficient which is a severely ill-posed problem. We regularize this problem by combining quasi-boundary value method and quasi-reversibility method and then obtain sharp error estimate between the exact solution and the regularized solution. A numerical experiment is given in order to illustrate our results.http://dx.doi.org/10.1155/2012/943621 |
| spellingShingle | Pham Hoang Quan Le Minh Triet Dang Duc Trong A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient International Journal of Mathematics and Mathematical Sciences |
| title | A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient |
| title_full | A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient |
| title_fullStr | A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient |
| title_full_unstemmed | A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient |
| title_short | A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient |
| title_sort | regularization of the backward problem for nonlinear parabolic equation with time dependent coefficient |
| url | http://dx.doi.org/10.1155/2012/943621 |
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