Scholarlink

<p>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 <i>t</i><sup>−<i>α</i></sup> as <i>t</i> goes to infinity.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

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

  • 期刊论文

  • 发表日期：

    2025年1月1日

查看全文
  • Zhiyuan Li,
  • Xinchi Huang,
  • Masahiro Yamamoto

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.