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Blow-up for discrete reaction-diffusion equations on networks

Chung Soon-Yeong (Sogang University, Department of Mathematics and Program of Integrated Biotechnology, Seoul, Republic of Korea)
Lee Jae-Hwang (Sogang University, Department of Mathematics, Seoul, Republic of Korea)

In this paper, we discuss the conditions under which blow-up occurs for the solutions of reaction-diffusion equations on networks. The analysis of this class of problems includes the existence of blow-up in finite time and the determination of the blow-up time and the corresponding blow-up rate. In addition, when the solution blows up, we give estimates for the blow-up time and also provide the blow-up rate. Finally, we show some numerical illustrations which describe the main results.

Keywords: reaction-diffusion, discrete Laplacian, comparison principle, blow-up