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The modeling error of well treatment for unsteady flow in porous media
| 1. | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, China |
References:
| [1] |
L. O. Aleksandrovna, S. V. Alekseevich and U. N. Nikolaevna, Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence, R.I., 1968. |
| [2] |
D. Alain and L. Ta-Tsien, Comportement limite des solutions de certains problèmes mixtes pour les équations paraboliques, J. Math. Pures Appl., 61 (1982), 113-130. |
| [3] |
D. Alain and L. Ta-Tsien, Comportement limite des solutions de certains problèmes mixtes pour des équations paraboliques (II), Acta Math. Sci., 2 (1982), 85-104. |
| [4] |
R. A. Alessandra, Hölder regularity results for solutions of parabolic equations, in Variational Analysis and Applications, Nonconvex Optim. Appl., 79, Springer, New York, 2005, 921-934.
doi: 10.1007/0-387-24276-7_53. |
| [5] |
L. Daqian, Z. Songmu, T. Yongji, S. Hanji, G. Ruxi and S. Weixi, Boundary value problmes with equivalued surface boundary conditions for self-adjoint elliptic differential equations I, Journal of Fudan University, (1976), 61-71. |
| [6] |
L. Daqian, Z. Songmu, T. Yongji, S. Hanji, G. Ruxi and S. Weixi, Boundary value problmes with equivalued surface boundary conditions for self-adjoint elliptic differential equations II, Journal of Fudan University, (1976), 136-145. |
| [7] |
L. P. K. Daniel and E. Lars, Numerical solution of first-kind Volterra equations by sequential Tikhonov regularization, SIAM J. Numer. Anal., 34 (1997), 1432-1450.
doi: 10.1137/S003614299528081X. |
| [8] |
L. P. K. Daniel, A survey of regularization methods for first-kind Volterra equations, in Surveys on Solution Methods for Inverse Problems, Springer, Vienna, 2000, 53-82. |
| [9] |
A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations, $2^{nd}$ edition, Chapman & Hall/CRC, Boca Raton, FL, 2008.
doi: 10.1201/9781420010558. |
| [10] |
P. H. Valvatne, J. Serve, L. J. Durlofsky and K. Aziza, Efficient modeling of nonconventional wells with downhole inflow control devices, Journal of Petroleum Science and Engineering, 39 (2003), 99-116.
doi: 10.1016/S0920-4105(03)00042-1. |
| [11] |
S. Weixi, On mixed initial-boundary value problmes of second order parabolic equations with equivalued surface boundary conditions, Journal of Fudan University, (1978), 15-24. |
| [12] |
C. Zhangxin, H. Guanren and M. Yuanle, Computational Science and Engineering, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2006. |
| [13] |
C. Zhiming and Y. Xingye, Numerical homogenization of well singularities in the flow transport through heterogeneous porous media, Multiscale Model. Simul., 1 (2003), 260-303.
doi: 10.1137/S1540345902413322. |
show all references
References:
| [1] |
L. O. Aleksandrovna, S. V. Alekseevich and U. N. Nikolaevna, Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence, R.I., 1968. |
| [2] |
D. Alain and L. Ta-Tsien, Comportement limite des solutions de certains problèmes mixtes pour les équations paraboliques, J. Math. Pures Appl., 61 (1982), 113-130. |
| [3] |
D. Alain and L. Ta-Tsien, Comportement limite des solutions de certains problèmes mixtes pour des équations paraboliques (II), Acta Math. Sci., 2 (1982), 85-104. |
| [4] |
R. A. Alessandra, Hölder regularity results for solutions of parabolic equations, in Variational Analysis and Applications, Nonconvex Optim. Appl., 79, Springer, New York, 2005, 921-934.
doi: 10.1007/0-387-24276-7_53. |
| [5] |
L. Daqian, Z. Songmu, T. Yongji, S. Hanji, G. Ruxi and S. Weixi, Boundary value problmes with equivalued surface boundary conditions for self-adjoint elliptic differential equations I, Journal of Fudan University, (1976), 61-71. |
| [6] |
L. Daqian, Z. Songmu, T. Yongji, S. Hanji, G. Ruxi and S. Weixi, Boundary value problmes with equivalued surface boundary conditions for self-adjoint elliptic differential equations II, Journal of Fudan University, (1976), 136-145. |
| [7] |
L. P. K. Daniel and E. Lars, Numerical solution of first-kind Volterra equations by sequential Tikhonov regularization, SIAM J. Numer. Anal., 34 (1997), 1432-1450.
doi: 10.1137/S003614299528081X. |
| [8] |
L. P. K. Daniel, A survey of regularization methods for first-kind Volterra equations, in Surveys on Solution Methods for Inverse Problems, Springer, Vienna, 2000, 53-82. |
| [9] |
A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations, $2^{nd}$ edition, Chapman & Hall/CRC, Boca Raton, FL, 2008.
doi: 10.1201/9781420010558. |
| [10] |
P. H. Valvatne, J. Serve, L. J. Durlofsky and K. Aziza, Efficient modeling of nonconventional wells with downhole inflow control devices, Journal of Petroleum Science and Engineering, 39 (2003), 99-116.
doi: 10.1016/S0920-4105(03)00042-1. |
| [11] |
S. Weixi, On mixed initial-boundary value problmes of second order parabolic equations with equivalued surface boundary conditions, Journal of Fudan University, (1978), 15-24. |
| [12] |
C. Zhangxin, H. Guanren and M. Yuanle, Computational Science and Engineering, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2006. |
| [13] |
C. Zhiming and Y. Xingye, Numerical homogenization of well singularities in the flow transport through heterogeneous porous media, Multiscale Model. Simul., 1 (2003), 260-303.
doi: 10.1137/S1540345902413322. |
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