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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2512.15164 |
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| _version_ | 1866908739846537216 |
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| author | Antil, Harbir Mizuno, Daiki Shirakawa, Ken Ukai, Naotaka |
| author_facet | Antil, Harbir Mizuno, Daiki Shirakawa, Ken Ukai, Naotaka |
| contents | This paper develops a general mathematical framework for pseudo-parabolic gradient systems with state-dependent dynamics. The state dependence is induced by variable coefficient fields in the governing energy functional. Such coefficients arise naturally in scientific and technological models, including state-dependent mobilities in KWC-type grain boundary motion and variable orientation-adaptation operators in anisotropic image denoising. We establish two main results: the existence of energy-dissipating solutions, and the uniqueness and continuous dependence on initial data. The proposed framework yields a general well-posedness theory for a broad class of nonlinear evolutionary systems driven by state-dependent operators. As illustrative applications, we present an anisotropic image-denoising model and a new pseudo-parabolic KWC-type model for anisotropic grain boundary motion, and prove that both fit naturally within the abstract structure of $(\mathrm{S})_ν$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-Posedness of Pseudo-Parabolic Gradient Systems with State-Dependent Dynamics Antil, Harbir Mizuno, Daiki Shirakawa, Ken Ukai, Naotaka Analysis of PDEs 35K52, 35K70, 37L05 This paper develops a general mathematical framework for pseudo-parabolic gradient systems with state-dependent dynamics. The state dependence is induced by variable coefficient fields in the governing energy functional. Such coefficients arise naturally in scientific and technological models, including state-dependent mobilities in KWC-type grain boundary motion and variable orientation-adaptation operators in anisotropic image denoising. We establish two main results: the existence of energy-dissipating solutions, and the uniqueness and continuous dependence on initial data. The proposed framework yields a general well-posedness theory for a broad class of nonlinear evolutionary systems driven by state-dependent operators. As illustrative applications, we present an anisotropic image-denoising model and a new pseudo-parabolic KWC-type model for anisotropic grain boundary motion, and prove that both fit naturally within the abstract structure of $(\mathrm{S})_ν$. |
| title | Well-Posedness of Pseudo-Parabolic Gradient Systems with State-Dependent Dynamics |
| topic | Analysis of PDEs 35K52, 35K70, 37L05 |
| url | https://arxiv.org/abs/2512.15164 |