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 | References | Similar Articles | Additional Information
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