On a nonlinear hyperbolic problem arising in two-phase flows in naturally fractured reservoirs |
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Authors: | Hermano Frid |
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Institution: | (1) Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Cep 21945, RJ, Brasil |
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Abstract: | A system of two first-order quasilinear equations consisting of one nonhomogenous hyperbolic conservation law and an ordinary differential equation is investigated in two spatial dimensions. The initial boundary-value problem is solved for the system and existence, uniqueness, and stability theorems are proved. We also obtain a result on the behavior of the solution when time goes to infinity which agrees with practical experience. These results offer mathematical validation to computer models in current usage for the numerical simulation of multiphase flow in naturally fractured reservoirs. |
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Keywords: | 35L40 76S05 |
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