Second order evolutionary partial differential variational-like inequalities

Imran Ali; Faizan Ahmad Khan; Haider Abbas Rizvi; Rais Ahmad; Arvind Kumar Rajpoot; Imran Ali; Faizan Ahmad Khan; Haider Abbas Rizvi; Rais Ahmad; Arvind Kumar Rajpoot

doi:10.3934/math.2022924

AIMS Mathematics

2022, Volume 7, Issue 9: 16832-16850. doi: 10.3934/math.2022924

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Second order evolutionary partial differential variational-like inequalities

1.
Department of Mathematics, School of Advanced Sciences, Kalasalingam Academy of Research and Education, Anand Nagar, Kirshanankoil-626126, India
2.
Computational & Analytical Mathematics and Their Applications Research Group, Faculty of Science, University of Tabuk, Tabuk-71491, Saudi Arabia
3.
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India

Received: 16 April 2022 Revised: 06 July 2022 Accepted: 06 July 2022 Published: 14 July 2022
MSC : 49J27, 90C30, 49J40

This work is dedicated to the study of a second order evolutionary partial differential variational-like inequality in Banach space. We obtain the mild solution of our problem by applying the concept of strongly continuous cosine family of bounded linear operators, fixed point theorem for condensing multi-valued operators and measure of non-compactness. It is proved that the solution set of mixed variational-like inequalities is non-empty, bounded, closed and convex.
- second order evolution equation,
- variational-like inequality,
- cosine family,
- measure of non-compactness,
- mild solution
Citation: Imran Ali, Faizan Ahmad Khan, Haider Abbas Rizvi, Rais Ahmad, Arvind Kumar Rajpoot. Second order evolutionary partial differential variational-like inequalities[J]. AIMS Mathematics, 2022, 7(9): 16832-16850. doi: 10.3934/math.2022924

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Abstract

This work is dedicated to the study of a second order evolutionary partial differential variational-like inequality in Banach space. We obtain the mild solution of our problem by applying the concept of strongly continuous cosine family of bounded linear operators, fixed point theorem for condensing multi-valued operators and measure of non-compactness. It is proved that the solution set of mixed variational-like inequalities is non-empty, bounded, closed and convex.

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