Issue |
ESAIM: COCV
Volume 29, 2023
|
|
---|---|---|
Article Number | 2 | |
Number of page(s) | 35 | |
DOI | https://doi.org/10.1051/cocv/2022087 | |
Published online | 11 January 2023 |
Existence of variational solutions to nonlocal evolution equations via convex minimization
1
Tata Institute of Fundamental Research, Centre for Applicable Mathematics,
Bangalore
560065,
Karnataka,
India
2
School of Interwoven Arts and Sciences, Krea University,
Sri City
517646,
India
* Corresponding author: vivek.tewary@krea.edu.in
Received:
6
September
2022
Accepted:
13
December
2022
We prove existence of variational solutions for a class of nonlocal evolution equations whose prototype is the double phase equation
The approach of minimization of parameter-dependent convex functionals over space-time trajectories requires only appropriate convexity and coercivity assumptions on the nonlocal operator. As the parameter tends to zero, we recover variational solutions. Under further growth conditions, these variational solutions are global weak solutions. Further, this provides a direct minimization approach to approximation of nonlocal evolution equations.
Mathematics Subject Classification: 35K51 / 35A01 / 35A15 / 35R11
Key words: Nonlocal operators with nonstandard growth / elliptic regularization / Parabolic systems / parabolic minimizers / evolutionary variational solutions
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.