On the existence and uniqueness of weak solutions to time-fractional elliptic equations with time-dependent variable coefficients

Tuan, Hoang

doi:10.1090/proc/15533

On the existence and uniqueness of weak solutions to time-fractional elliptic equations with time-dependent variable coefficients
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by Hoang The Tuan

Proc. Amer. Math. Soc. 149 (2021), 2597-2608

DOI: https://doi.org/10.1090/proc/15533

Published electronically: March 29, 2021

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Abstract:

This paper is devoted to discussing the existence and uniqueness of weak solutions to time-fractional elliptic equations having time-dependent variable coefficients. To obtain the main result, our strategy is to combine the Galerkin method, a basic inequality for the fractional derivative of convex Lyapunov candidate functions, the Yoshida approximation sequence and the weak compactness argument.

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