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

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.

Published
2019-12-27
How to Cite
GUSWANTO, Bambang Hendriya; BIN ADMON, Mohd. Ariff; BINTI LIM BOON CHYE, Nur Natasha. THE EXISTENCE AND UNIQUENESS OF THE MILD SOLUTION TO A NONLINEAR CAUCHY PROBLEM ASSOCIATED WITH A NONLOCAL REACTION-DIFFUSION SYSTEM. Jurnal Ilmiah Matematika dan Pendidikan Matematika, [S.l.], v. 11, n. 2, p. 19-28, dec. 2019. ISSN 2550-0422. Available at: <http://jos.unsoed.ac.id/index.php/jmp/article/view/2264>. Date accessed: 25 feb. 2020.