An inverse problem for linear system of dispersive equations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914057203744768 |
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| author | Pizo, Deissy Marcela Grajales, Juan Carlos Muñoz |
| author_facet | Pizo, Deissy Marcela Grajales, Juan Carlos Muñoz |
| contents | This paper addresses the inverse problem of identifying the linear velocity coefficient in a linear system governed by two Benjamin-Bona-Mahony-type equations, which model the displacement of water waves propagating along the surface of a shallow channel, incorporating effects of dispersion and topography. To solve this, we reformulate the inverse problem as a restricted minimization problem (RMP), aimed at optimizing a suitably regularized objective functional. We use numerical techniques, specifically the iterative L-BFGS-B algorithm implemented in the Dolfin-Adjoint-Python-SciPy libraries, to solve the RMP effectively. Following methodologies similar to those in Pipicano et al., we establish a local stability result for the RMP. Additionally, through numerical simulations, we demonstrate the effectiveness of the proposed identification method in determining the linear velocity coefficient in Boussinesq-type systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21524 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An inverse problem for linear system of dispersive equations Pizo, Deissy Marcela Grajales, Juan Carlos Muñoz Analysis of PDEs This paper addresses the inverse problem of identifying the linear velocity coefficient in a linear system governed by two Benjamin-Bona-Mahony-type equations, which model the displacement of water waves propagating along the surface of a shallow channel, incorporating effects of dispersion and topography. To solve this, we reformulate the inverse problem as a restricted minimization problem (RMP), aimed at optimizing a suitably regularized objective functional. We use numerical techniques, specifically the iterative L-BFGS-B algorithm implemented in the Dolfin-Adjoint-Python-SciPy libraries, to solve the RMP effectively. Following methodologies similar to those in Pipicano et al., we establish a local stability result for the RMP. Additionally, through numerical simulations, we demonstrate the effectiveness of the proposed identification method in determining the linear velocity coefficient in Boussinesq-type systems. |
| title | An inverse problem for linear system of dispersive equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.21524 |