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Optimal control of fractional diffusion with Dirac measures

  • Enrique Otarola
  • Abner J. Salgado
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Abstract

We study a PDE-constrained optimization problem for an elliptic equation with the spectral fractional Laplacian and a linear combination of Dirac measures as the forcing term; the controls are the amplitudes of these singular sources. We prove existence and uniqueness of an optimal solution and derive first-order optimality conditions. We then propose a discretization based on finite elements. Since the set of admissible controls is finite dimensional, the control variable itself does not require discretization. We conclude by deriving a priori error bounds

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Cite

BibTeXRIS
BibTeX
@misc{otarola2026optimal,
  title = {{Optimal control of fractional diffusion with Dirac measures}},
  author = {Enrique Otarola and Abner J. Salgado},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.27776},
  eprint = {2608.27776},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.27776},
}
RIS
TY  - UNPB
TI  - Optimal control of fractional diffusion with Dirac measures
AU  - Enrique Otarola
AU  - Abner J. Salgado
PY  - 2026
DA  - 2026/08/27
PB  - arXiv
DO  - 10.48550/arxiv.2608.27776
UR  - https://arxiv.org/abs/2608.27776
AB  - We study a PDE-constrained optimization problem for an elliptic equation with the spectral fractional Laplacian and a linear combination of Dirac measures as the forcing term; the controls are the amplitudes of these singular sources. We prove existence and uniqueness of an optimal solution and derive first-order optimality conditions. We then propose a discretization based on finite elements. Since the set of admissible controls is finite dimensional, the control variable itself does not require discretization. We conclude by deriving a priori error bounds
ER  -