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


Author: Hoang The Tuan
Journal: Proc. Amer. Math. Soc. 149 (2021), 2597-2608
MSC (2020): Primary 26A33, 35R11, 35Dxx, 34A12
DOI: https://doi.org/10.1090/proc/15533
Published electronically: March 29, 2021
MathSciNet review: 4246810
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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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Additional Information

Hoang The Tuan
Affiliation: Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307 Ha Noi, Viet Nam
MR Author ID: 1016449
Email: httuan@math.ac.vn

Received by editor(s): October 15, 2020
Received by editor(s) in revised form: December 25, 2020, and January 12, 2021
Published electronically: March 29, 2021
Additional Notes: This research was supported by The International Center for Research and Postgraduate Training in Mathematics–Institute of Mathematics–Vietnam Academy of Science and Technology under the Grant ICRTM01-2020.09. A part of this paper was completed while the author was a postdoc at the Vietnam Institute for Advanced Study in Mathematics (VIASM). He would like to thank VIASM for their support and hospitality.
Communicated by: Wenxian Shen
Article copyright: © Copyright 2021 American Mathematical Society