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Fuzzy solutions for general hyperbolic partial differential equations with local initial conditions

In this paper, we study the existence and uniqueness of fuzzy solutions for general hyperbolic partial differential equations with local conditions making use of the Banach fixed point theorem. Some examples are presented to illustrate our results. | JOURNAL OF SCIENCE OF HNUE Mathematical and Physical Sci. 2013 Vol. 58 No. 7 pp. 27-38 This paper is available online at http stdb.hnue.edu.vn FUZZY SOLUTIONS FOR GENERAL HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH LOCAL INITIAL CONDITIONS Nguyen Thi My Ha1 Nguyen Thi Kim Son2 and Ha Thi Thanh Tam3 1 Faculty of Mathematics Hai Phong University 2 Faculty of Mathematics Hanoi National University of Education 3 Diem Dien High School Thai Binh Abstract. In this paper we study the existence and uniqueness of fuzzy solutions for general hyperbolic partial differential equations with local conditions making use of the Banach fixed point theorem. Some examples are presented to illustrate our results. Keywords Hyperbolic differential equations fuzzy solution local conditions fixed point. 1. Introduction Fuzzy set theory was first introduced by Zadeh 15 . The ambition of fuzzy set theory is to provide a formal setting for incomplete inexact vague and uncertain information. Today after its conception fuzzy set theory has become a fashionable theory used in many branches of real life such as dynamics computer technology biological phenomena and financial forecasting etc. The concepts of fuzzy sets fuzzy numbers fuzzy metric spaces fuzzy valued functions and the necessary calculus of fuzzy functions have been investigated in papers 3 7-10 . The fuzzy derivative was first introduced by Chang and Zadeh in 5 . The study of differential equations was considerd in 12-14 . The recent results on fuzzy differential equations and inclusion was presented in the monograph of Lakshmikantham and Mohapatra 11 . Nowadays many fields of science can be presented using mathematical models especially partial differential equations. When databases that are transformed from real life into mathematical models are incomplete or vague we often use fuzzy partial differential equations. Hence more and more authors have studied solutions for fuzzy partial differential equations. In 4 Buckley and .