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Kurzweil's impulsive inverse problem for the Kelvin--Voigt equations with p-Laplacian

  • Stanislav Antontsev
  • Pardeep Kumar
  • Ivan Kuznetsov
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Abstract

In the present paper, we proceed with the research initiated in (S. Antontsev \emph{et al.}, Inverse Problems, 2021). We study the inverse problem for the Kelvin--Voigt equations with p-Laplacian and with a right-hand side in the integral over-determination condition, which approximates a discontinuous function at t=0. We rescale the problem in a neighbourhood [0,1/n] and pass to the limit as n approaches infinity. This leads to the inverse problem on an infinitesimal initial layer, which transforms the initial velocity into a new one.

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Cite

BibTeXRIS
BibTeX
@misc{antontsev2026kurzweils,
  title = {{Kurzweil's impulsive inverse problem for the Kelvin--Voigt equations with $p$-Laplacian}},
  author = {Stanislav Antontsev and Pardeep Kumar and Ivan Kuznetsov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27950},
  eprint = {2610.27950},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27950},
}
RIS
TY  - UNPB
TI  - Kurzweil's impulsive inverse problem for the Kelvin--Voigt equations with p-Laplacian
AU  - Stanislav Antontsev
AU  - Pardeep Kumar
AU  - Ivan Kuznetsov
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27950
UR  - https://arxiv.org/abs/2610.27950
AB  - In the present paper, we proceed with the research initiated in (S. Antontsev \emph{et al.}, Inverse Problems, 2021). We study the inverse problem for the Kelvin--Voigt equations with p-Laplacian and with a right-hand side in the integral over-determination condition, which approximates a discontinuous function at t=0. We rescale the problem in a neighbourhood [0,1/n] and pass to the limit as n approaches infinity. This leads to the inverse problem on an infinitesimal initial layer, which transforms the initial velocity into a new one.
ER  -