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Local travelling wave solutions and self-similar solutions for a green roof model
| Content Provider | Semantic Scholar |
|---|---|
| Author | Alzahrani, A. K. |
| Copyright Year | 2014 |
| Abstract | In this thesis we study travelling wave solutions and self-similar solutions for a green roof model and for some simpler models which are derived from that model. We focus on two limiting cases near a dry region and near a saturated region. We start by considering a convection model in the absence of diffusion and sink terms. We show that rarefaction waves and shock solutions exist for several cases. Next, we consider a convection-diffusion model where both the convective and diffusive terms are present and we show that travelling wave solutions and self-similar solutions exist for some cases. Moreover, numerical simulations are used for the travelling wave and self-similar solutions and confirm the analytic predictions. Finally, we consider the green roof model where all terms are present and we show that travelling wave solutions exist, whereas self-similar solutions are not found. We also show the travelling wave solutions exist for the two limiting cases. Acknowledgements I would like to thank my supervisor, Prof. Andrew Lacey, whose encouragement, kind guidance and support from the initial to the final level enabled me to develop an understanding of the subject. His extensive knowledge has played a crucial role in the development of this thesis. Without his help and advice, this thesis could not have been completed. He could not even realize how much I have learned from him. I am also extremely grateful to my second supervisor, Dr. Lubomir Banas, for his help with numerical simulations. I wish also to thank the other members of staff of the Department of Mathematics for their help and support. I must express my gratitude to my wife Hamidah and my sons Yazan and Murad for their love, support and patience. My sincere thanks are due to my parents, brothers and sisters for continued support and encouragement me during my studies. Finally, I would like to thank the Department of Mathematics at King Abdulaziz University and Saudi Cultural Bureau in London for their funding support. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ros.hw.ac.uk/bitstream/handle/10399/2776/AlzahraniA_0714_macs.pdf?isAllowed=y&sequence=1 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
