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Uniqueness for an illposed reactiondispersion model. Application to organic pollution in streamwaters
1.  LMAC, EA 2222, Université de Technologie de Compiègne, BP 20529, 60205 COMPIEGNE Cedex, France 
References:
[1] 
R. A. Adams and J. J. F. Fournier, "Sobolev Spaces,'', Second edition, 140 (2003). Google Scholar 
[2] 
M. Andrle, F. Ben Belgacem and A. El Badia, Identification of moving pointwise sources in an advectiondispersionreaction equation,, Inverse Problems, 27 (2011). doi: 10.1088/02665611/27/2/025007. Google Scholar 
[3] 
F. Ben Belgacem, Uniqueness for an illposed parabolic system,, Comptes Rendus Mathématique Acad. Sci. Paris, 349 (2011), 1161. doi: 10.1016/j.crma.2011.10.006. Google Scholar 
[4] 
A. Bermúdez, Mathematical techniques for some environmental problems related to water pollution control,, in, 27 (1993), 12. Google Scholar 
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C. Bernardi, C. Canuto and Y. Maday, Generalized infsup condition for Chebyshev spectral approximation of the Stokes problem,, SIAM J. Numer. Anal., 25 (1988), 1237. doi: 10.1137/0725070. Google Scholar 
[6] 
F. Brezzi and M. Fortin, "Mixed and Hybrid Finite Element Methods,'', Springer Series in Computational Mathematics, 15 (1991). Google Scholar 
[7] 
L. C. Brown and T. O. Barnwell, "The Enhanced Stream Water Quality Models QUAL2E and QUAL2EUNCAS: Documentation and User Manual,'', Environmental Protection Agency, (1987). Google Scholar 
[8] 
S. C. Chapra, "Applied Numerical Methods with MATLAB,'', McGrawHill, (2004). Google Scholar 
[9] 
J. Cousteix and J. Mauss, "Analyse Asymptotique et Couche Limite,'', Mathématiques et Applications, 56 (2006). Google Scholar 
[10] 
R. Dautray and J.L. Lions, "Mathematical Analyis and Numerical Methods for Science and Technology,'', Vol. 5, (1992). Google Scholar 
[11] 
W. Eckhaus, "Asymptotic Analysis of Singular Perturbations,'', Studies in Mathematics and its Applications, 9 (1979). Google Scholar 
[12] 
A. El Badia, T. HaDuong and A. Hamdi, Identification of a point source in a linear advectiondispersionreaction equation: Application to a pollution source problem,, Inverse Problems, 21 (2005), 1121. doi: 10.1088/02665611/21/3/020. Google Scholar 
[13] 
A. El Badia and A. Hamdi, Inverse source problem in an advectiondispersionreaction system: Application to water pollution,, Inverse Problems, 23 (2007), 2103. doi: 10.1088/02665611/23/5/017. Google Scholar 
[14] 
D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order,'', Second edition, 224 (1983). Google Scholar 
[15] 
G. Gripenberg, S.O. London and O. Steffans, "Volterra Integral and Functional Equations,'', Encyclopedia of Mathematics and its Applications, 34 (1990). Google Scholar 
[16] 
A. Hamdi, Identification of a timevarying point source in a system of two coupled linear diffusionadvectionreaction equations: Application to surface water pollution,, Inverse Problems, 25 (2009). doi: 10.1088/02665611/25/11/115009. Google Scholar 
[17] 
A. Hamdi, The recovery of a timedependent point source in a linear transport equation: Application to surface water pollution,, Inverse Problems, 25 (2009). doi: 10.1088/02665611/25/7/075006. Google Scholar 
[18] 
G. Jolánkai, "Basic River Water Quality Models: Computer Aided Learning (CAL) Programme on Water Quality Modelling (WQMCAL),'', International Hydrological Programme, (1213). Google Scholar 
[19] 
J.L. Lions and E. Magenes, "Problèmes aux Limites Non Homogènes et Applications,'', Dunod, (1968). Google Scholar 
[20] 
G. I. Marchuk, "Mathematical Models in Environmental Problems,'', Encyclopedia of Mathematics and its Applications, 34 (1986). Google Scholar 
[21] 
A. Okubo, "Diffusion and Ecological Problems: Mathematical Models,'', An extended version of the Japanese edition, 10 (1980). Google Scholar 
[22] 
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,'', Applied Mathematical Sciences, 44 (1983). Google Scholar 
[23] 
J.C. Saut and B. Scheurer, Unique continuation for some evolution equations,, Journal of Differential Equations, 66 (1987), 118. doi: 10.1016/00220396(87)90043X. Google Scholar 
[24] 
C. N. Sawyer, P. L. McCarty and G. F. Parkin, "Chemistry for Environmental Engineering and Science,'', Unpublished proceedings of the Delaware Conference on Ill Posed Inverse Problems, (1980). Google Scholar 
[25] 
G. Wahba, "Ill Posed Problems: Numerical and Statistical Methods for Mildly, Moderately and Severely Ill Posed Problems With Noisy Data,'', McGrawHill, (2003). Google Scholar 
show all references
References:
[1] 
R. A. Adams and J. J. F. Fournier, "Sobolev Spaces,'', Second edition, 140 (2003). Google Scholar 
[2] 
M. Andrle, F. Ben Belgacem and A. El Badia, Identification of moving pointwise sources in an advectiondispersionreaction equation,, Inverse Problems, 27 (2011). doi: 10.1088/02665611/27/2/025007. Google Scholar 
[3] 
F. Ben Belgacem, Uniqueness for an illposed parabolic system,, Comptes Rendus Mathématique Acad. Sci. Paris, 349 (2011), 1161. doi: 10.1016/j.crma.2011.10.006. Google Scholar 
[4] 
A. Bermúdez, Mathematical techniques for some environmental problems related to water pollution control,, in, 27 (1993), 12. Google Scholar 
[5] 
C. Bernardi, C. Canuto and Y. Maday, Generalized infsup condition for Chebyshev spectral approximation of the Stokes problem,, SIAM J. Numer. Anal., 25 (1988), 1237. doi: 10.1137/0725070. Google Scholar 
[6] 
F. Brezzi and M. Fortin, "Mixed and Hybrid Finite Element Methods,'', Springer Series in Computational Mathematics, 15 (1991). Google Scholar 
[7] 
L. C. Brown and T. O. Barnwell, "The Enhanced Stream Water Quality Models QUAL2E and QUAL2EUNCAS: Documentation and User Manual,'', Environmental Protection Agency, (1987). Google Scholar 
[8] 
S. C. Chapra, "Applied Numerical Methods with MATLAB,'', McGrawHill, (2004). Google Scholar 
[9] 
J. Cousteix and J. Mauss, "Analyse Asymptotique et Couche Limite,'', Mathématiques et Applications, 56 (2006). Google Scholar 
[10] 
R. Dautray and J.L. Lions, "Mathematical Analyis and Numerical Methods for Science and Technology,'', Vol. 5, (1992). Google Scholar 
[11] 
W. Eckhaus, "Asymptotic Analysis of Singular Perturbations,'', Studies in Mathematics and its Applications, 9 (1979). Google Scholar 
[12] 
A. El Badia, T. HaDuong and A. Hamdi, Identification of a point source in a linear advectiondispersionreaction equation: Application to a pollution source problem,, Inverse Problems, 21 (2005), 1121. doi: 10.1088/02665611/21/3/020. Google Scholar 
[13] 
A. El Badia and A. Hamdi, Inverse source problem in an advectiondispersionreaction system: Application to water pollution,, Inverse Problems, 23 (2007), 2103. doi: 10.1088/02665611/23/5/017. Google Scholar 
[14] 
D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order,'', Second edition, 224 (1983). Google Scholar 
[15] 
G. Gripenberg, S.O. London and O. Steffans, "Volterra Integral and Functional Equations,'', Encyclopedia of Mathematics and its Applications, 34 (1990). Google Scholar 
[16] 
A. Hamdi, Identification of a timevarying point source in a system of two coupled linear diffusionadvectionreaction equations: Application to surface water pollution,, Inverse Problems, 25 (2009). doi: 10.1088/02665611/25/11/115009. Google Scholar 
[17] 
A. Hamdi, The recovery of a timedependent point source in a linear transport equation: Application to surface water pollution,, Inverse Problems, 25 (2009). doi: 10.1088/02665611/25/7/075006. Google Scholar 
[18] 
G. Jolánkai, "Basic River Water Quality Models: Computer Aided Learning (CAL) Programme on Water Quality Modelling (WQMCAL),'', International Hydrological Programme, (1213). Google Scholar 
[19] 
J.L. Lions and E. Magenes, "Problèmes aux Limites Non Homogènes et Applications,'', Dunod, (1968). Google Scholar 
[20] 
G. I. Marchuk, "Mathematical Models in Environmental Problems,'', Encyclopedia of Mathematics and its Applications, 34 (1986). Google Scholar 
[21] 
A. Okubo, "Diffusion and Ecological Problems: Mathematical Models,'', An extended version of the Japanese edition, 10 (1980). Google Scholar 
[22] 
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,'', Applied Mathematical Sciences, 44 (1983). Google Scholar 
[23] 
J.C. Saut and B. Scheurer, Unique continuation for some evolution equations,, Journal of Differential Equations, 66 (1987), 118. doi: 10.1016/00220396(87)90043X. Google Scholar 
[24] 
C. N. Sawyer, P. L. McCarty and G. F. Parkin, "Chemistry for Environmental Engineering and Science,'', Unpublished proceedings of the Delaware Conference on Ill Posed Inverse Problems, (1980). Google Scholar 
[25] 
G. Wahba, "Ill Posed Problems: Numerical and Statistical Methods for Mildly, Moderately and Severely Ill Posed Problems With Noisy Data,'', McGrawHill, (2003). Google Scholar 
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