Shape Design for Degenerate Parabolic Equations with Degenerate Boundaries and Its Application to Boundary Observability
Analysis of PDEs
2026-05-20 v1 Optimization and Control
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.
Keywords
Cite
@article{arxiv.2605.19599,
title = {Shape Design for Degenerate Parabolic Equations with Degenerate Boundaries and Its Application to Boundary Observability},
author = {Dong-Hui Yang and Bao-Zhu Guo},
journal= {arXiv preprint arXiv:2605.19599},
year = {2026}
}