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arXiv · 2203.10448

Well-posedness of initial-boundary value problem for time-fractional diffusion-wave equation with time-dependent coefficients

Xinchi Huang·Masahiro Yamamoto
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Abstract

We consider the well-posedness of the initial-boundary value problem for a time-fractional partial differential equation with the fractional order lying in (1,2]. For the case of time-dependent coefficients, it is difficult to give an explicit solution formula by the eigenfunction expansion method. In order to deal with the case of time-varying coefficients, we first show the unique existence and regularity of solution to a system of time-fractional ordinary differential equations. Then the unique existence of the weak solution to the time-fractional partial differential equation and improved regularity are derived by using the Galerkin method.

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Xinchi Huang, Masahiro Yamamoto. 2022-03-20. Well-posedness of initial-boundary value problem for time-fractional diffusion-wave equation with time-dependent coefficients. https://arxiv.org/abs/2203.10448

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