ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Blow-up of Solutions to Reaction-diffusion System with Nonstandard Growth Conditions

Journal of Applied Nonlinear Dynamics 6(3) (2017) 407--425 | DOI:10.5890/JAND.2017.09.008

Arumugam Gurusamy$^{1}$; Krishnan Balachandran$^{2}$

$^{1}$ Computational Biology Division, DRDO-BU CLS, Bharathiar University Campus, Coimbatore- 641046, INDIA

$^{2}$ Department of Mathematics, Bharathiar University, Coimbatore - 641 046, INDIA

Abstract

This paper is concerned with the existence and blow-up of solutions of reaction diffusion system with p(x)− growth conditions. The existence of weak solution is proved by using the Galerkin method. The blow-up of solutions is established by applying the method of comparison with suitable blow-up of self-similar subsolutions. Finally the theoretical results are illustrated by numerical examples.

Acknowledgments

This work is supported by Defence Research and Development Organization(DRDO), New Delhi, Government of India.

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