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arXiv · 2605.19599

Shape Design for Degenerate Parabolic Equations with Degenerate Boundaries and Its Application to Boundary Observability

Dong-Hui Yang·Bao-Zhu Guo
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Abstract

In this study, we firstly establish the well-posedness of a degenerate parabolic equation under Dirichlet boundary conditions. Following this, we introduce a shape design problem, which acts as a framework for approximating the degenerate parabolic equation through a series of uniformly parabolic equations. Finally, as a tangible application of this shape design approach, we deduce a boundary observability inequality associated with the degenerate parabolic equation.

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Dong-Hui Yang, Bao-Zhu Guo. 2026-05-19. Shape Design for Degenerate Parabolic Equations with Degenerate Boundaries and Its Application to Boundary Observability. https://arxiv.org/abs/2605.19599

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