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PreprintCC BY 4.0arXiv

Large-Time Behavior of Pseudo-Parabolic Equations Associated with Generalized Total Variation Energies

  • Daisuke Kubota
  • Daiki Mizuno
  • Ken Shirakawa
  • Naotaka Ukai
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Abstract

In this paper, we study the well-posedness and large-time behavior of a pseudo-parabolic problem associated with a generalized total variation energy in the BV-framework. A main mathematical issue arises from the mismatch between the Sobolev regularity of solutions at finite times and the BV-structure of the corresponding steady-state problem. We prove the existence and uniqueness of solutions and investigate the relationship between their large-time behavior and solutions to the steady-state problem. Moreover, our results include the convergence of the solution trajectory to the unique steady-state solution under a typical setting arising in image processing.

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Cite

BibTeXRIS
BibTeX
@misc{kubota2026largetime,
  title = {{Large-Time Behavior of Pseudo-Parabolic Equations Associated with Generalized Total Variation Energies}},
  author = {Daisuke Kubota and Daiki Mizuno and Ken Shirakawa and Naotaka Ukai},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12583},
  eprint = {2609.12583},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12583},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Large-Time Behavior of Pseudo-Parabolic Equations Associated with Generalized Total Variation Energies
AU  - Daisuke Kubota
AU  - Daiki Mizuno
AU  - Ken Shirakawa
AU  - Naotaka Ukai
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12583
UR  - https://arxiv.org/abs/2609.12583
AB  - In this paper, we study the well-posedness and large-time behavior of a pseudo-parabolic problem associated with a generalized total variation energy in the BV-framework. A main mathematical issue arises from the mismatch between the Sobolev regularity of solutions at finite times and the BV-structure of the corresponding steady-state problem. We prove the existence and uniqueness of solutions and investigate the relationship between their large-time behavior and solutions to the steady-state problem. Moreover, our results include the convergence of the solution trajectory to the unique steady-state solution under a typical setting arising in image processing.
ER  -