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PreprintCC BY-SA 4.0arXiv

Stable determination of damping and potential coefficients in a semilinear wave equation

  • Rahul Bhardwaj
  • Mandeep Kumar
  • Manmohan Vashisth
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Abstract

We consider an inverse problem for a semilinear wave equation with time-independent damping, linear potential, and nonlinear potential coefficients in a bounded domain of ℝn for n≥ 2. The main objective is to establish stability estimates for the simultaneous recovery of these coefficients from the associated Dirichlet-to-Neumann map. Our approach combines second-order linearization with suitably constructed geometric optics and asymptotic solutions. We establish Hölder-type stability estimates for the recovery of each of the three coefficients appearing in the semilinear wave equation under suitable a priori bounds on these coefficients. To the best of our knowledge, this is the first stability result for simultaneous determination of time-independent damping, linear and nonlinear potentials in a semiliner wave equation.

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Cite

BibTeXRIS
BibTeX
@misc{bhardwaj2026stable,
  title = {{Stable determination of damping and potential coefficients in a semilinear wave equation}},
  author = {Rahul Bhardwaj and Mandeep Kumar and Manmohan Vashisth},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08951},
  eprint = {2609.08951},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08951},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Stable determination of damping and potential coefficients in a semilinear wave equation
AU  - Rahul Bhardwaj
AU  - Mandeep Kumar
AU  - Manmohan Vashisth
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08951
UR  - https://arxiv.org/abs/2609.08951
AB  - We consider an inverse problem for a semilinear wave equation with time-independent damping, linear potential, and nonlinear potential coefficients in a bounded domain of ℝ^n for n≥ 2. The main objective is to establish stability estimates for the simultaneous recovery of these coefficients from the associated Dirichlet-to-Neumann map. Our approach combines second-order linearization with suitably constructed geometric optics and asymptotic solutions. We establish Hölder-type stability estimates for the recovery of each of the three coefficients appearing in the semilinear wave equation under suitable a priori bounds on these coefficients. To the best of our knowledge, this is the first stability result for simultaneous determination of time-independent damping, linear and nonlinear potentials in a semiliner wave equation.
ER  -