International Journal of Differential Equations

Blow-Up Solution of Modified-Logistic-Diffusion Equation

P. Sitompul and Y. Soeharyadi

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Modified-Logistic-Diffusion Equation ut=Duxx+u|1-u| with Neumann boundary condition has a global solution, if the given initial condition ψ satisfies ψ(x)1, for all x[0,1]. Other initial conditions can lead to another type of solutions; i.e., an initial condition that satifies 01ψ(x)dx>1 will cause the solution to blow up in a finite time. Another initial condition will result in another kind of solution, which depends on the diffusion coefficient D. In this paper, we obtained the lower bound of D, so that the solution of Modified-Logistic-Diffusion Equation with a given initial condition will have a global solution.

Article information

Int. J. Differ. Equ., Volume 2019 (2019), Article ID 7205865, 6 pages.

Received: 31 July 2018
Revised: 19 October 2018
Accepted: 19 November 2018
First available in Project Euclid: 26 February 2019

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Sitompul, P.; Soeharyadi, Y. Blow-Up Solution of Modified-Logistic-Diffusion Equation. Int. J. Differ. Equ. 2019 (2019), Article ID 7205865, 6 pages. doi:10.1155/2019/7205865.

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