Data assimilation and null controllability of degenerate/singular parabolic problems
Date
2017-05-17
Authors
Atifi, Khalid
Essoufi, El-Hassan
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Data assimilation, Null controllability, Regularization, Heat equation, Inverse problem, Degenerate equations, Optimization
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.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.