Well-Posedness and Asymptotic Estimate for a Diffusion Equation with Time-Fractional Derivative  

作　　者：Zhiyuan LI Xinchi HUANG Masahiro YAMAMOTO 

机构地区：[1]School of Mathematics and Statistics,Ningbo University,Ningbo 315211,Zhejiang,China [2]Corresponding author.Graduate School of Science,The University of Tokyo,Tokyo,Japan [3]Graduate School of Mathematical Sciences,The University of Tokyo,Tokyo,Japan [4]Honorary Member of Academy of Romanian Scientists,Bucuresti,Romania [5]Correspondence member of Accademia Peloritana dei Pericolanti,Palazzo Universita,Messina,Italy

出　　处：《Chinese Annals of Mathematics,Series B》2025年第1期115-138,共24页数学年刊(B辑英文版)

基　　金：supported by the National Natural Science Foundation of China(Nos.12271277,11771270,11801326,91730303);the Japan Society for the Promotion of Science(Nos.20H00117,20F20319);A3 Foresight Program“Modeling and Computation of Applied Inverse Problems”of Japan Society for the Promotion of Science and the Research Institute for Mathematical Sciences,an International Joint Usage/Research Center located in Kyoto University。

摘　　要：In this paper,the authors study the well-posedness and the asymptotic estimate of solution for a mixed-order time-fractional diffusion equation in a bounded domain subject to the homogeneous Dirichlet boundary condition.Firstly,the unique existence and regularity estimates of solution to the initial-boundary value problem are considered.Then combined with some important properties,including a maximum principle for a time-fractional ordinary equation and a coercivity inequality for fractional derivatives,the energy method shows that the decay in time of the solution is dominated by the term t-α as t goes to infinity.

关 键 词：Mixed-order fractional diffusion equation Initial-boundary value problem Asymptotic estimate Energy method 

分 类 号：O175[理学—数学]