Decay estimates and extinction properties of parabolic equations with classical and fractional time derivatives

• Published in: Electronic journal of differential equations Vol. 2025; no. 1-??; p. 89
• Main Authors: Meng, Fanmeng, Zhou, Xian-Feng
• Format: Journal Article
• Language: English
• Published: 16.09.2025
• ISSN: 1072-6691; 1072-6691
• DOI: 10.58997/ejde.2025.89

In this article, we study the decay estimates and extinction properties of weak solutions to some parabolic equations with classical and fractional time derivatives. Firstly, we establish a new comparison principle for parabolic equations with mixed time derivatives. Based on this comparison principle and energy methods, we obtain the power-law decay estimates for weak solutions of nonhomogeneous abstract parabolic problems with mixed time-derivatives. Furthermore, we present three specific applications of the decay results for the abstract parabolic problem.  Finally, we discus the finite time extinction property of the weak solution for the 1-Kirchhoff type parabolic problem with mixed time-derivatives. For more information see https://ejde.math.txstate.edu/Volumes/2025/89/abstr.html