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arXiv · 2604.15991

The Biharmonic Heat Equation with General Dynamic Boundary Conditions

S. E. Chorfi·F. Et-tahri·L. Maniar
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Abstract

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.

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S. E. Chorfi, F. Et-tahri, L. Maniar. 2026-04-17. The Biharmonic Heat Equation with General Dynamic Boundary Conditions. https://arxiv.org/abs/2604.15991

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