Weak solution of non-Newtonian polytropic variational inequality in fresh agricultural product supply chain problem

Abstract

In this article, we study a class of variational inequality problems with non-Newtonian polytropic parabolic operators. We introduce a mapping with an adjustable parameter to control the polytropic term, which exactly meets the conditions of Leray-Schauder fixed point theory. At the same time, we construct a penalty function to transform the variational inequality into a regular parabolic initial boundary value problem. Thus, the existence is treated with a Leray-Schauder fixed point theory as well as a suitable version of Aubin-Lions lemma. Then, the uniqueness and stability of the solution are analyzed.

Keywords

• variational inequality problem
• generalized solution
• non-newtonian polytropic operator
• existence
• uniqueness and stability
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