Homogenization of parabolic problem with nonlinear transmission condition |
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| Institution: | 1. Laboratoire de Mathématiques et Applications, Université Sultan Moulay Slimane, Faculté des Sciences et Techniques, B.P.523, Béni-Mellal, Morocco;2. Laboratoire de Mathématiques Jean Leray UMR6629 CNRS / Université de Nantes 2 rue de la Houssinière, BP92208 44322 Nantes, France;1. Research Center on Mathematical Modelling (MODEMAT), Escuela Politécnica Nacional, Ladrón de Guevara E11-253, Quito, Ecuador;2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, CB3 0WA, Cambridge, United Kingdom;1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, PR China;2. College of Mathematics and Statistics, Chongqing University, Chongqing 400044, PR China |
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| Abstract: | In this paper, we investigate the periodic homogenization of nonlinear parabolic equation arising from heat exchange in composite material problems. This problem, defined in periodical domain, is nonlinear at the interface. This nonlinearity models the heat radiation on the interface, which constitutes the transmission boundary conditions, between the two components of the material. The main challenge is, first, to show the well-posedness of the microscopic problem using the topological degree of Leray–Schauder tools. Then, we apply the two scale convergence to identify the equivalent macroscopic model using homogenization techniques. Finally, in order to confirm the efficiency of the homogenization process, we present some numerical results obtained via finite element approximation. |
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| Keywords: | Homogenization Nonlinear parabolic coupled problem Heat transfer Composite medium Two scale convergence |
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