Variational approach to reaction–diffusion process
A variational formulation is established for the reaction–diffusion equation, and an analytical solution is obtained which is valid for the whole solution domain. The variational method is proved to be effective and simple.
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| Published in | Physics letters. A Vol. 368; no. 3; pp. 263 - 265 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
20.08.2007
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| Subjects | |
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| Abstract | A variational formulation is established for the reaction–diffusion equation, and an analytical solution is obtained which is valid for the whole solution domain. The variational method is proved to be effective and simple. |
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| AbstractList | A variational formulation is established for the reaction–diffusion equation, and an analytical solution is obtained which is valid for the whole solution domain. The variational method is proved to be effective and simple. |
| Author | Mo, Lu-Feng |
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A contributor: fullname: He – volume: 29 start-page: 108 year: 2006 ident: bib003 publication-title: Chaos Solitons Fractals contributor: fullname: Wu – volume: 350 start-page: 342 year: 2006 ident: bib018 publication-title: Phys. Lett. A contributor: fullname: Gao – volume: 358 start-page: 121 year: 2006 ident: bib015 publication-title: Phys. Lett. A contributor: fullname: Bhattacharjeet – volume: 354 start-page: 437 year: 2006 ident: bib017 publication-title: Phys. Lett. A contributor: fullname: Qu – volume: 20 start-page: 1141 year: 2006 ident: bib014 publication-title: Int. J. Mod. Phys. B contributor: fullname: He – volume: 30 start-page: 700 year: 2006 ident: bib010 publication-title: Chaos Solitons Fractals contributor: fullname: Wu – volume: 355 start-page: 337 year: 2006 ident: bib009 publication-title: Phys. Lett. A contributor: fullname: Ganji – volume: 357 start-page: 319 year: 2006 ident: bib016 publication-title: Phys. Lett. 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Non-Linear Mech. doi: 10.1016/S0020-7462(98)00048-1 contributor: fullname: He – volume: 30 start-page: 700 issue: 3 year: 2006 ident: 10.1016/j.physleta.2007.04.005_bib010 publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2006.03.020 contributor: fullname: He – volume: 27 start-page: 376 issue: 4 year: 2004 ident: 10.1016/j.physleta.2007.04.005_bib011 publication-title: Chem. Eng. Technol. doi: 10.1002/ceat.200401872 contributor: fullname: He – volume: 27 start-page: 1119 issue: 5 year: 2006 ident: 10.1016/j.physleta.2007.04.005_bib004 publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2005.04.113 contributor: fullname: Momani – volume: 358 start-page: 121 issue: 2 year: 2006 ident: 10.1016/j.physleta.2007.04.005_bib015 publication-title: Phys. Lett. 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| Title | Variational approach to reaction–diffusion process |
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