Monotone iterative method of upper and lower solutions applied to a multilayer combustion model in porous media |
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| Institution: | 1. School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, People’s Republic of China;2. NAAM Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics, Faculty of Art and Sciences, Cankaya University, Balgat 06530, Ankara, Turkey;4. Institute of Space Sciences, Magurele-Bucharest, Romania;1. Institute of Automation and Control Processes, Far Eastern Branch of the Russian Academy of Sciences, 5 Radio St., Vladivostok, 690041, Russia;2. Far Eastern Federal University, 8 Sukhanova St., Vladivostok, 690091, Russia;3. Institute of Problems of Chemical Physics, Russian Academy of Sciences, 1 Academician Semenov Ave., Chernogolovka, Moscow region, 142432, Russia |
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| Abstract: | This paper presents a new nonlinear reaction–diffusion–convection system coupled with a system of ordinary differential equations that models a combustion front in a multilayer porous medium. The model includes heat transfer between the layers and heat loss to the external environment. A few assumptions are made to simplify the model, such as incompressibility; then, the unknowns are determined to be the temperature and fuel concentration in each layer. When the fuel concentration in each layer is a known function, we prove the existence and uniqueness of a classical solution for the initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. We construct monotone iterations of upper and lower solutions and prove that these iterations converge to a unique solution for the problem, first locally and then, in time, globally. |
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| Keywords: | Reaction–diffusion–convection system Upper and lower solutions Combustion Multilayer porous medium |
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