|
|
| |
| Well-Posedness and Asymptotic Estimate for a Diffusion Equation with Time-Fractional Derivative |
| |
Citation： |
Zhiyuan LI,Xinchi HUANG,Masahiro YAMAMOTO.Well-Posedness and Asymptotic Estimate for a Diffusion Equation with Time-Fractional Derivative[J].Chinese Annals of Mathematics B,2025,46(1):115~138 |
| Page view： 168
Net amount： 110 |
Authors： |
Zhiyuan LI; Xinchi HUANG;Masahiro YAMAMOTO |
Foundation： |
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. |
|
|
| Abstract： |
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. |
Keywords： |
Mixed-order fractional diffusion equation Initial-boundary value problem Asymptotic estimate Energy method |
Classification： |
35R11, 35B40, 26A33, 34A08, 35B50 |
|
|
Download PDF Full-Text
|
|
|
|
