# On a Generalized Fisher Equation

(2010) On a Generalized Fisher Equation. Masters thesis, King Fahd University of Petroleum and Minerals.

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## Arabic Abstract

ﻦﻣ ًﺍﺮﻴﺜﻛ ﻒﺼﺗ ﻲﺘﻟﺍﻭ ﺮﺸﻴﻓ ﺔﻟﺩﺎﻌﻤﺑ ﺔﻓﻭﺮﻌﻤﻟﺍ ﺭﺎﺸﺘﻧﻻﺍ ﻞﻌﻓ ﺩﺭ ﺔﻟﺩﺎﻌﻣ ﺔﻟﺎﺳﺮﻟﺍ ﻩﺬﻫ ﻲﻓ ﺱﺭﺪﻧ ﺮﻴﻏ ﻢﻴﻤﻌﺗ ﻰﻠﻋ ﺔﺳﺍﺭﺪﻟﺍ ﺰﻛﺮﺗ .ﺎﻫﺮﻴﻏﻭ ءﺎﻴﺣﻷﺍﻭ ﻲﻧﺎﻜﺴﻟﺍ ﻮﻤﻨﻟﺍﻭ ﺔﺛﺍﺭﻮﻟﺍ ﻢﻠﻋ ﻝﺎﺠﻣ ﻲﻓ ﻞﻛﺎﺸﻤﻟﺍ ﻥﺃ ﺽﺮﺘﻔﻧ ."ﻲﻟ ﺮﻅﺎﻨﺗ" ﺭﻮﻈﻨﻣ ﻦﻣ ﻱﺮﻄﻗ ﻞﺛﺎﻤﺘﺑ ﺔﻴﻧﺍﻮﻄﺳﻻﺍ ﺭﻭﺎﺤﻤﻟﺍ ﻡﺍﺪﺨﺘﺳﺎﺑ ﺔﻟﺩﺎﻌﻤﻟﺍ ﻩﺬﻬﻟ ﻲﻄﺧ ﺎﻨﻠﺼﺣﻭ ﺭﺎﺸﺘﻧﻻﺍ ﺔﻟﺍﺩ ﻒﻴﻨﺼﺗ ﺔﻟﻭﺎﺤﻣ ﺖﻤﺗ .ﻊﺑﺎﺘﻟﺍ ﺮﻴﻐﺘﻤﻟﺍ ﻲﻓ ﻝﺍﻭﺩ ﺎﻤﻫ ﻞﻋﺎﻔﺘﻟﺍﻭ ﺔﻳﺭﺎﺸﺘﻧﻻﺍ ﻱﺪﺣ ﺮﻴﻐﺘﻤﻟﺍ ﻰﻠﻋ ﺔﻳﺭﺎﺸﺘﻧﻻﺍ ﺩﺎﻤﺘﻋﺍ ﺔﻟﺎﺣ ﻲﻓ ﻑﻭﺮﻌﻤﻟﺍ ﻞﺤﻟﺍ ﻥﺃ ﺎﻧﺪﺟﻭ .ﺕﻻﺎﺤﻟﺍ ﺾﻌﺒﻟ ﺔﻣﺎﺗ ﻝﻮﻠﺣ ﻰﻠﻋ ﺔﻳﺭﺎﺸﺘﻧﻻﺍ ﻢﻜﺤﻳ ﻱﺬﻟﺍ ﺓﻮﻘﻟﺍ ﻥﻮﻧﺎﻗ ﻥﺃ ﺎﻧﺪﺟﻭ .ﺔﺳﺍﺭﺪﻟﺍ ﻩﺬﻫ ﻲﻓ ﻡﺎﻌﻟﺍ ﺎﻨﻠﺣ ﻦﻣ ﺔﺻﺎﺧ ﺔﻟﺎﺣ ﻥﻮﻜﻳ ﻊﺑﺎﺘﻟﺍ ﻦﻣ ﺔﻳﺮﻔﺼﻟﺍ ﺔﺟﺭﺪﻟﺍ ﻦﻣ "ﻞﺴﻴﺑ" ﻪﻟﺍﺪﻟ ﻲﻄﺧ ﺐﻴﻛﺮﺘﻟ ﺐﺳﺎﻨﻤﻟﺍ ﺭﺬﺠﻟﺍ ﻞﻜﺷ ﻰﻠﻋ ﻡﺎﺗ ﻞﺣ ﻰﻟﺇ ﻱﺩﺆﻳ .ﺔﻴﻄﺧ ﺔﻟﺍﺩ ﻦﻋ ﺓﺭﺎﺒﻋ ﺔﻳﺭﺎﺸﺘﻧﻻﺍ ﺖﻧﺎﻛ ﺍﺫﺇ ﻞﻋﺎﻔﺘﻟﺍ ﺪﺣ ﻒﻴﻨﺼﺗ ﻦﻜﻤﻳ ﻚﻟﺫ ﻊﻣﻭ .ﻲﻧﺎﺜﻟﺍﻭ ﻝﻭﻷﺍ ﻉﻮﻨﻟﺍ .ﺮﻅﺎﻨﺗ ﺩﻮﺟﻭ ﻡﺪﻋ ﺔﻟﺎﺣ ﻲﻓ ﻢﻋﺃ ﻞﻜﺸﺑ ﻒﻴﻨﺼﺗ ﻰﻟﺇ ﺩﻮﻘﺗ ﻥﺃ ﻦﻜﻤﻳ ﺔﺳﺍﺭﺪﻟﺍ ﻩﺬﻫ

## English Abstract

We consider a reaction diusion equation known as the Fisher equation which models problems in genetics, population growth and mathematical biology among others. A generalized non-linear form of this equation in cylindrical coordinates with radial sym- metry is studied from Lie symmetry point of view. The diusivity and the reaction terms are assumed to be functions of the dependent variable. An attempt to classify the diusivity function is made and exact solutions are obtained in some cases. The known results in case of diusivity being proportional to the dependent variable are shown to be a special case of our analysis. It is found that the power law dependence of diusivity function leads to exact solution in the form of the respective root of a linear combination of the Bessel function of order zero of rst and the second kind. However, the reaction term can be classied if the diusivity is a linear function. The study can lead to a classication in the most general settings in which no radial symmetry is present.

Item Type: Thesis (Masters) Math College of Computing and Mathematics > Mathematics Zaman, Fiazud Messaoudi, Salim and Furati, Khaled and Saleh, khairul (g200602940) 25 May 2010 09:12 01 Nov 2019 14:12 https://eprints.kfupm.edu.sa/id/eprint/136286