On initial inverse problem for nonlinear couple heat with Kirchhoff type
Abstract The main objective of the paper is to study the final model for the Kirchhoff-type parabolic system. Such type problems have many applications in physical and biological phenomena. Under some smoothness of the final Cauchy data, we prove that the problem has a unique mild solution. The main...
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2021
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oai:doaj.org-article:0f13b9935dc34f77973b04dea43904af2021-12-05T12:07:12ZOn initial inverse problem for nonlinear couple heat with Kirchhoff type10.1186/s13662-021-03655-81687-1847https://doaj.org/article/0f13b9935dc34f77973b04dea43904af2021-12-01T00:00:00Zhttps://doi.org/10.1186/s13662-021-03655-8https://doaj.org/toc/1687-1847Abstract The main objective of the paper is to study the final model for the Kirchhoff-type parabolic system. Such type problems have many applications in physical and biological phenomena. Under some smoothness of the final Cauchy data, we prove that the problem has a unique mild solution. The main tool is Banach’s fixed point theorem. We also consider the non-well-posed problem in the Hadamard sense. Finally, we apply truncation method to regularize our problem. The paper is motivated by the work of Tuan, Nam, and Nhat [Comput. Math. Appl. 77(1):15–33, 2019].Danh Hua Quoc NamSpringerOpenarticleKirchhoff-type problemsNonlocal problemWell-posednessRegularizationMathematicsQA1-939ENAdvances in Difference Equations, Vol 2021, Iss 1, Pp 1-15 (2021) |
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DOAJ |
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DOAJ |
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| topic |
Kirchhoff-type problems Nonlocal problem Well-posedness Regularization Mathematics QA1-939 |
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Kirchhoff-type problems Nonlocal problem Well-posedness Regularization Mathematics QA1-939 Danh Hua Quoc Nam On initial inverse problem for nonlinear couple heat with Kirchhoff type |
| description |
Abstract The main objective of the paper is to study the final model for the Kirchhoff-type parabolic system. Such type problems have many applications in physical and biological phenomena. Under some smoothness of the final Cauchy data, we prove that the problem has a unique mild solution. The main tool is Banach’s fixed point theorem. We also consider the non-well-posed problem in the Hadamard sense. Finally, we apply truncation method to regularize our problem. The paper is motivated by the work of Tuan, Nam, and Nhat [Comput. Math. Appl. 77(1):15–33, 2019]. |
| format |
article |
| author |
Danh Hua Quoc Nam |
| author_facet |
Danh Hua Quoc Nam |
| author_sort |
Danh Hua Quoc Nam |
| title |
On initial inverse problem for nonlinear couple heat with Kirchhoff type |
| title_short |
On initial inverse problem for nonlinear couple heat with Kirchhoff type |
| title_full |
On initial inverse problem for nonlinear couple heat with Kirchhoff type |
| title_fullStr |
On initial inverse problem for nonlinear couple heat with Kirchhoff type |
| title_full_unstemmed |
On initial inverse problem for nonlinear couple heat with Kirchhoff type |
| title_sort |
on initial inverse problem for nonlinear couple heat with kirchhoff type |
| publisher |
SpringerOpen |
| publishDate |
2021 |
| url |
https://doaj.org/article/0f13b9935dc34f77973b04dea43904af |
| work_keys_str_mv |
AT danhhuaquocnam oninitialinverseproblemfornonlinearcoupleheatwithkirchhofftype |
| _version_ |
1718372237219725312 |