Observation estimates for a semilinear heat equation in ℝⁿ

2025/03/17 by Zheng, Guojie, Yu, Xin
#35K15 #93B07 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2503.12951

Abstract

This paper studies the state observation problems for the semilinear heat equation in Rⁿ. We derive observation estimates for the equation using the logarithmic convexity property of the frequency function (see [12]). As an application, we show that if two solutions coincide on a nonempty open subset ω⊂Ωat some time T>0, then they must be identical.

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