Evolutionary problems driven by variational inequalities with multiple integral functionals

Savin Treanţă; Muhammad Bilal Khan; Soubhagya Kumar Sahoo; Thongchai Botmart; Savin Treanţă; Muhammad Bilal Khan; Soubhagya Kumar Sahoo; Thongchai Botmart

doi:10.3934/math.2023075

AIMS Mathematics

2023, Volume 8, Issue 1: 1488-1508. doi: 10.3934/math.2023075

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Research article

Evolutionary problems driven by variational inequalities with multiple integral functionals

1.
Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
2.
Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
3.
Fundamental Sciences Applied in Engineering Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania
4.
Department of Mathematics, COMSATS University Islamabad, 44000 Islamabad, Pakistan
5.
Department of Mathematics, Institute of Technical Education and Research, Siksha O Anusandhan University, Bhubaneswar 751030, Odisha, India
6.
Department of Mathematics, Faculty of Science, Khon Kaen University, 40002 Khoon Kaen, Thailand
Correction on: AIMS Mathematics 8: 13791-13792.

Received: 18 August 2022 Revised: 26 September 2022 Accepted: 10 October 2022 Published: 21 October 2022
MSC : 49J40, 65K10, 26B25, 49K20

In this paper, the authors focus on extending the well-known weak sharp solutions for variational inequalities to a controlled variational-type inequality governed by convex multiple integral functionals. Simultaneously, some equivalent conditions on weak sharpness associated with solutions of the considered inequality are obtained by using the minimum principle sufficiency property.
Citation: Savin Treanţă, Muhammad Bilal Khan, Soubhagya Kumar Sahoo, Thongchai Botmart. Evolutionary problems driven by variational inequalities with multiple integral functionals[J]. AIMS Mathematics, 2023, 8(1): 1488-1508. doi: 10.3934/math.2023075

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Abstract

In this paper, the authors focus on extending the well-known weak sharp solutions for variational inequalities to a controlled variational-type inequality governed by convex multiple integral functionals. Simultaneously, some equivalent conditions on weak sharpness associated with solutions of the considered inequality are obtained by using the minimum principle sufficiency property.

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