Work

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

Year: 2025

Type: article

Abstract: 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

Source: Electronic Journal of Differential Equations

DOI: 10.58997/ejde.2025.89

Authors: Fanmeng Meng, Xian-Feng Zhou

Institution: Anhui University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Anhui Jianzhu University

Awards: 关于分数阶偏泛函微分方程基本理论的研究, G6773887705