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Research Article | Open Access

Second order evolutionary partial differential variational-like inequalities

Imran Ali1( ), Faizan Ahmad Khan2( ), Haider Abbas Rizvi1, Rais Ahmad3, Arvind Kumar Rajpoot3
Department of Mathematics, School of Advanced Sciences, Kalasalingam Academy of Research and Education, Anand Nagar, Kirshanankoil-626126, India
Computational & Analytical Mathematics and Their Applications Research Group, Faculty of Science, University of Tabuk, Tabuk-71491, Saudi Arabia
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
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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.

Keywords

second order evolution equationvariational-like inequalitycosine familymeasure of non-compactnessmild solution
CLC number: 49J27, 90C30, 49J40

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 16832-16850
DOI: 10.3934/math.2022924

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Cite this article:
Ali I, Khan FA, Rizvi HA, et al. Second order evolutionary partial differential variational-like inequalities. AIMS Mathematics, 2022, 7(9): 16832-16850. https://doi.org/10.3934/math.2022924

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Received: 16 April 2022
Revised: 06 July 2022
Accepted: 06 July 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)