## International Journal of Differential Equations

### Blow-Up Solution of Modified-Logistic-Diffusion Equation

#### Abstract

Modified-Logistic-Diffusion Equation ${u}_{t}=D{u}_{xx}+u|\mathrm{1}-u|$ with Neumann boundary condition has a global solution, if the given initial condition $\psi$ satisfies $\psi (x)\le \mathrm{1}$, for all $x\in [\mathrm{0,1}]$. Other initial conditions can lead to another type of solutions; i.e., an initial condition that satifies ${\int }_{\mathrm{0}}^{\mathrm{1}}\psi (x)dx>\mathrm{1}$ 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

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

Dates
Revised: 19 October 2018
Accepted: 19 November 2018
First available in Project Euclid: 26 February 2019

https://projecteuclid.org/euclid.ijde/1551150359

Digital Object Identifier
doi:10.1155/2019/7205865

#### Citation

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. https://projecteuclid.org/euclid.ijde/1551150359

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