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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, (1968).
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[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.
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[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.
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[4] |
R. A. Alessandra, Hölder regularity results for solutions of parabolic equations,, in Variational Analysis and Applications, (2005), 921.
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. Google Scholar |
[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. Google Scholar |
[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.
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, (2000), 53.
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[9] |
A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations,, $2^{nd}$ edition, (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.
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. Google Scholar |
[12] |
C. Zhangxin, H. Guanren and M. Yuanle, Computational Science and Engineering,, Society for Industrial and Applied Mathematics, (2006).
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[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.
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, (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.
|
[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.
|
[4] |
R. A. Alessandra, Hölder regularity results for solutions of parabolic equations,, in Variational Analysis and Applications, (2005), 921.
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. Google Scholar |
[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. Google Scholar |
[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.
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, (2000), 53.
|
[9] |
A. D. Polyanin and A. V. Manzhirov, Handbook of Integral Equations,, $2^{nd}$ edition, (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.
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. Google Scholar |
[12] |
C. Zhangxin, H. Guanren and M. Yuanle, Computational Science and Engineering,, Society for Industrial and Applied Mathematics, (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.
doi: 10.1137/S1540345902413322. |
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