-
Previous Article
On the Budyko-Sellers energy balance climate model with ice line coupling
- DCDS-B Home
- This Issue
-
Next Article
Exponential stability of solutions to impulsive stochastic differential equations driven by $G$-Brownian motion
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. |
| [1] |
Yoshihiro Shibata. Global well-posedness of unsteady motion of viscous incompressible capillary liquid bounded by a free surface. Evolution Equations and Control Theory, 2018, 7 (1) : 117-152. doi: 10.3934/eect.2018007 |
| [2] |
Shenglan Xie, Maoan Han, Peng Zhu. A posteriori error estimate of weak Galerkin fem for second order elliptic problem with mixed boundary condition. Discrete and Continuous Dynamical Systems - B, 2021, 26 (10) : 5217-5226. doi: 10.3934/dcdsb.2020340 |
| [3] |
Tong Li. Well-posedness theory of an inhomogeneous traffic flow model. Discrete and Continuous Dynamical Systems - B, 2002, 2 (3) : 401-414. doi: 10.3934/dcdsb.2002.2.401 |
| [4] |
Qi An, Chuncheng Wang, Hao Wang. Analysis of a spatial memory model with nonlocal maturation delay and hostile boundary condition. Discrete and Continuous Dynamical Systems, 2020, 40 (10) : 5845-5868. doi: 10.3934/dcds.2020249 |
| [5] |
Yueding Yuan, Zhiming Guo, Moxun Tang. A nonlocal diffusion population model with age structure and Dirichlet boundary condition. Communications on Pure and Applied Analysis, 2015, 14 (5) : 2095-2115. doi: 10.3934/cpaa.2015.14.2095 |
| [6] |
Kenji Nakanishi, Hideo Takaoka, Yoshio Tsutsumi. Local well-posedness in low regularity of the MKDV equation with periodic boundary condition. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 1635-1654. doi: 10.3934/dcds.2010.28.1635 |
| [7] |
Long Fan, Cheng-Jie Liu, Lizhi Ruan. Local well-posedness of solutions to the boundary layer equations for compressible two-fluid flow. Electronic Research Archive, 2021, 29 (6) : 4009-4050. doi: 10.3934/era.2021070 |
| [8] |
Abraham Sylla. Influence of a slow moving vehicle on traffic: Well-posedness and approximation for a mildly nonlocal model. Networks and Heterogeneous Media, 2021, 16 (2) : 221-256. doi: 10.3934/nhm.2021005 |
| [9] |
K. Domelevo. Well-posedness of a kinetic model of dispersed two-phase flow with point-particles and stability of travelling waves. Discrete and Continuous Dynamical Systems - B, 2002, 2 (4) : 591-607. doi: 10.3934/dcdsb.2002.2.591 |
| [10] |
Paola Goatin, Sheila Scialanga. Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity. Networks and Heterogeneous Media, 2016, 11 (1) : 107-121. doi: 10.3934/nhm.2016.11.107 |
| [11] |
Asim Aziz, Wasim Jamshed. Unsteady MHD slip flow of non Newtonian power-law nanofluid over a moving surface with temperature dependent thermal conductivity. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 617-630. doi: 10.3934/dcdss.2018036 |
| [12] |
W. Layton, R. Lewandowski. On a well-posed turbulence model. Discrete and Continuous Dynamical Systems - B, 2006, 6 (1) : 111-128. doi: 10.3934/dcdsb.2006.6.111 |
| [13] |
Muhammad Mansha Ghalib, Azhar Ali Zafar, Zakia Hammouch, Muhammad Bilal Riaz, Khurram Shabbir. Analytical results on the unsteady rotational flow of fractional-order non-Newtonian fluids with shear stress on the boundary. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 683-693. doi: 10.3934/dcdss.2020037 |
| [14] |
Haibo Cui, Qunyi Bie, Zheng-An Yao. Well-posedness in critical spaces for a multi-dimensional compressible viscous liquid-gas two-phase flow model. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1395-1410. doi: 10.3934/dcdsb.2018156 |
| [15] |
Hongjie Dong, Dapeng Du. Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space. Discrete and Continuous Dynamical Systems, 2008, 21 (4) : 1095-1101. doi: 10.3934/dcds.2008.21.1095 |
| [16] |
Luc Molinet, Francis Ribaud. On global well-posedness for a class of nonlocal dispersive wave equations. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 657-668. doi: 10.3934/dcds.2006.15.657 |
| [17] |
Manas Bhatnagar, Hailiang Liu. Well-posedness and critical thresholds in a nonlocal Euler system with relaxation. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 5271-5289. doi: 10.3934/dcds.2021076 |
| [18] |
Steinar Evje, Kenneth H. Karlsen. Hyperbolic-elliptic models for well-reservoir flow. Networks and Heterogeneous Media, 2006, 1 (4) : 639-673. doi: 10.3934/nhm.2006.1.639 |
| [19] |
Yogiraj Mantri, Michael Herty, Sebastian Noelle. Well-balanced scheme for gas-flow in pipeline networks. Networks and Heterogeneous Media, 2019, 14 (4) : 659-676. doi: 10.3934/nhm.2019026 |
| [20] |
Carlos F. Daganzo. On the variational theory of traffic flow: well-posedness, duality and applications. Networks and Heterogeneous Media, 2006, 1 (4) : 601-619. doi: 10.3934/nhm.2006.1.601 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]