The Biharmonic Heat Equation with General Dynamic Boundary Conditions
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arXiv
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| Format: | Preprint |
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2026
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| author | Chorfi, S. E. Et-tahri, F. Maniar, L. |
| author_facet | Chorfi, S. E. Et-tahri, F. Maniar, L. |
| contents | In this work, we initiate the study of the biharmonic heat equation in a spatial bounded domain subject to dynamic boundary conditions involving the bi-Laplace-Beltrami operator on the boundary. The boundary heat equation is coupled to the interior one via a normal derivative term. By combining the sesquilinear form method and semigroup theory, we establish substantial qualitative properties of the fourth-order parabolic equation; in particular, the self-adjointness of the associated operator, compactness of its resolvent, and further spectral properties. We also investigate the generation of a $C_0$-semigroup and analyze its main properties: analyticity, compactness, eventual positivity, and eventual $L^\infty$-contractivity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_15991 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Biharmonic Heat Equation with General Dynamic Boundary Conditions Chorfi, S. E. Et-tahri, F. Maniar, L. Analysis of PDEs Functional Analysis 35K35, 35A15, 47D06, 35B65 In this work, we initiate the study of the biharmonic heat equation in a spatial bounded domain subject to dynamic boundary conditions involving the bi-Laplace-Beltrami operator on the boundary. The boundary heat equation is coupled to the interior one via a normal derivative term. By combining the sesquilinear form method and semigroup theory, we establish substantial qualitative properties of the fourth-order parabolic equation; in particular, the self-adjointness of the associated operator, compactness of its resolvent, and further spectral properties. We also investigate the generation of a $C_0$-semigroup and analyze its main properties: analyticity, compactness, eventual positivity, and eventual $L^\infty$-contractivity. |
| title | The Biharmonic Heat Equation with General Dynamic Boundary Conditions |
| topic | Analysis of PDEs Functional Analysis 35K35, 35A15, 47D06, 35B65 |
| url | https://arxiv.org/abs/2604.15991 |