Mathematics and Statistics Vol. 7(5), pp. 182 - 190
DOI: 10.13189/ms.2019.070504
Reprint (PDF) (256Kb)

Evolutionary Variational Inequalities with Volterra Type Operators

Mykola Bokalo , Olha Sus ^*
Department of Mechanics and Mathematics, Ivan Franko National University of Lviv, Lviv, 79000, Ukraine

ABSTRACT

In this paper, we consider the initial-value problem for parabolic variational inequalities (subdifferential inclusions) with Volterra type operators. We prove the existence and the uniqueness of the solution. Furthermore, the estimates of the solution are obtained. The results are achieved using the Banach's fixed point theorem (the principle of compression mappings). The motivation for this work comes from the evolutionary variational inequalities arising in the study of frictionless contact problems for linear viscoelastic materials with long-term memory. Also, such kind of problems have their application in constructing different models of the injection molding processes.

KEYWORDS
Parabolic Variational Inequality, Variational Inclusion, Volterra Type Operators

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mykola Bokalo , Olha Sus , "Evolutionary Variational Inequalities with Volterra Type Operators," Mathematics and Statistics, Vol. 7, No. 5, pp. 182 - 190, 2019. DOI: 10.13189/ms.2019.070504.

(b). APA Format:
Mykola Bokalo , Olha Sus (2019). Evolutionary Variational Inequalities with Volterra Type Operators. Mathematics and Statistics, 7(5), 182 - 190. DOI: 10.13189/ms.2019.070504.