Blow-Up Solution of Modified-Logistic-Diffusion Equation
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...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2019/7205865 |
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| _version_ | 1832559101936140288 |
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| author | P. Sitompul Y. Soeharyadi |
| author_facet | P. Sitompul Y. Soeharyadi |
| author_sort | P. Sitompul |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d788e5abbcac41e5b8241ff3683cac3d |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-d788e5abbcac41e5b8241ff3683cac3d2025-02-03T01:30:51ZengWileyInternational Journal of Differential Equations1687-96431687-96512019-01-01201910.1155/2019/72058657205865Blow-Up Solution of Modified-Logistic-Diffusion EquationP. Sitompul0Y. Soeharyadi1State University of Medan, North Sumatra, IndonesiaBandung Institute of Technology, West Java, IndonesiaModified-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.http://dx.doi.org/10.1155/2019/7205865 |
| spellingShingle | P. Sitompul Y. Soeharyadi Blow-Up Solution of Modified-Logistic-Diffusion Equation International Journal of Differential Equations |
| title | Blow-Up Solution of Modified-Logistic-Diffusion Equation |
| title_full | Blow-Up Solution of Modified-Logistic-Diffusion Equation |
| title_fullStr | Blow-Up Solution of Modified-Logistic-Diffusion Equation |
| title_full_unstemmed | Blow-Up Solution of Modified-Logistic-Diffusion Equation |
| title_short | Blow-Up Solution of Modified-Logistic-Diffusion Equation |
| title_sort | blow up solution of modified logistic diffusion equation |
| url | http://dx.doi.org/10.1155/2019/7205865 |
| work_keys_str_mv | AT psitompul blowupsolutionofmodifiedlogisticdiffusionequation AT ysoeharyadi blowupsolutionofmodifiedlogisticdiffusionequation |