Analysis and Existence of Optimal Control of Diffusion Systems in Three Types of Products Alvian Alif Hidayatullah (a*), Anggi Lestari Lastiur Sitorus (a), Laylatus Syarifah (a), Subchan Subchan (a)
a) Department of Mathematics, Institut Teknologi Sepuluh Nopember, Surabaya, indonesia
*alvianalifhidayatullah[at]gmail.com
Abstract
Diffusion of innovation has an important role in the economic growth and progress of a country by spreading innovation through communication or other media in the social system. In the business environment, every company competes to present advantages and benefits in the products or services offered to achieve maximum profits. In everyday life, we often find products of the same type with different prices, quality and popularity, thus creating variations in consumer choices. Products with low prices can certainly be reached by various groups. However, products with high prices may not necessarily be accessible to various groups. It also doesn^t escape that some consumers are sometimes disappointed with a product. Therefore, in this research, a product innovation diffusion control model was constructed by providing control to each population of product users so that it does not move to a population that is disappointed with the product. There are several populations in this research, such as a population of non-users, a population of users of products with low prices, a population of users of products with high prices and a population who are disappointed with the product. This research discusses the analysis of positivity, uniqueness and the existence of optimal control in product diffusion control systems. Positivity is intended to indicate whether the model is valid, uniqueness indicates that the system has a unique solution, and the existence of optimal control aims to determine whether the product diffusion system model with control has optimal control or not.
Keywords: Diffusion of innovation- Positivity- Uniqueness- Existence of optimal control
