Volume 29, 2023
|Number of page(s)||35|
|Published online||11 January 2023|
Existence of variational solutions to nonlocal evolution equations via convex minimization
Tata Institute of Fundamental Research, Centre for Applicable Mathematics,
2 School of Interwoven Arts and Sciences, Krea University, Sri City 517646, India
* Corresponding author: email@example.com
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.
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