Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Vol 11 No 2 (2019): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)

THE EXISTENCE AND UNIQUENESS OF THE MILD SOLUTION TO A NONLINEAR CAUCHY PROBLEM ASSOCIATED WITH A NONLOCAL REACTION-DIFFUSION SYSTEM

Bambang Hendriya Guswanto (Universitas Jenderal Soedirman)
Mohd. Ariff Bin Admon (Universiti Teknologi Malaysia)
Nur Natasha Binti Lim Boon Chye (Universiti Tekonolgi Malaysia)

Article Info

Publish Date
27 Dec 2019

Abstract

We study the existence and uniqueness of a mild solution to a nonlinear Cauchy problem associated with a nonlocal reaction diffusion system by employing the properties of analytic semigroup operator generated by the linear part of the problem which is sectorial and then applying Banach Fixed Point Theorem to the problem. We show that the problem has a unique mild solution under a Lipschitz condition on the nonlinear part of the problem. An example as an application of the result obtained is also given.

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Journal Info
Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Website

Abbrev

jmp

Publisher

Universitas Jenderal Soedirman

Subject

Mathematics

Description

JMP is a an open access journal which publishes research articles, reviews, case studies, guest edited thematic issues and short communications/letters in all areas of mathematics, applied mathematics, applied commutative algebra and algebraic geometry, mathematical biology, physics and engineering, ...