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arXiv · 2609.12583

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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Daisuke Kubota, Daiki Mizuno, Ken Shirakawa, Naotaka Ukai. 2026-09-11. Large-Time Behavior of Pseudo-Parabolic Equations Associated with Generalized Total Variation Energies. https://arxiv.org/abs/2609.12583

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