Data assimilation and null controllability of degenerate/singular parabolic problems
| dc.contributor.author | Atifi, Khalid | |
| dc.contributor.author | Essoufi, El-Hassan | |
| dc.date.accessioned | 2022-05-17T14:24:22Z | |
| dc.date.available | 2022-05-17T14:24:22Z | |
| dc.date.issued | 2017-05-17 | |
| dc.description.abstract | In this article, we use the variational method in data assimilation to study numerically the null controllability of degenerate/singular parabolic problem ∂tψ - ∂x (xα∂xψ(x)) - λ/xβ ψ = ƒ, (x, t) ∈]0, 1[X]0, T[, ψ(x, 0) = ψ0, ψ|x=0 = ψ|x=1 = 0. To do this, we determine the source term ƒ with the aim of obtaining ψ(·, T) = 0, for all ψ0 ∈ L2(]0, 1[). This problem can be formulated in a least-squares framework, which leads to a non-convex minimization problem that is solved using a regularization approach. Also we present some numerical experiments. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 17 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Atifi, K., & Essoufi, E. H. (2017). Data assimilation and null controllability of degenerate/singular parabolic problems. <i>Electronic Journal of Differential Equations, 2017</i>(135), pp. 1-17. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15787 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Data assimilation | |
| dc.subject | Null controllability | |
| dc.subject | Regularization | |
| dc.subject | Heat equation | |
| dc.subject | Inverse problem | |
| dc.subject | Degenerate equations | |
| dc.subject | Optimization | |
| dc.title | Data assimilation and null controllability of degenerate/singular parabolic problems | |
| dc.type | Article |