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arXiv · 2511.05783

Stability of parabolic equations in non-cylindrical domains

Lingyang Liu
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Abstract

This paper addresses the stability of a class of parabolic equations in non-cylindrical domains. We investigate the $L^\infty$-stability of systems for both nondegenerate and degenerate cases. Unlike in cylindrical domains, solutions to such problems may not exhibit exponential decay. An interesting phenomenon observed is that degeneracy has a positive impact on $L^\infty$-norm estimates for solutions to the system.

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Lingyang Liu. 2025-11-08. Stability of parabolic equations in non-cylindrical domains. https://arxiv.org/abs/2511.05783

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