Stability of parabolic equations in non-cylindrical domains
Abstract
This paper addresses the stability of a class of parabolic equations in non-cylindrical domains. We investigate the L∞-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∞-norm estimates for solutions to the system.
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