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Identifying a space dependent coefficient in a reaction-diffusion equation
1. | Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, P.le Aldo Moro 5, 00185 Roma, Italy |
2. | Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy |
References:
[1] |
M. Choulli, An inverse problem for a semilinear parabolic equation, Inverse Problems, 10 (1994), 1123-1132.
doi: 10.1088/0266-5611/10/5/009. |
[2] |
M. Choulli and M. Yamamoto, An inverse parabolic problem with non-zero initial condition, Inverse Problems, 13 (1997), 19-27.
doi: 10.1088/0266-5611/13/1/003. |
[3] |
M. Choulli and M. Yamamoto, Uniqueness and stability in determining the heat radiative coefficient, the initial temperature and a boundary coefficient in a parabolic equation, Nonlinear Anal., 69 (2008), 3983-3998.
doi: 10.1016/j.na.2007.10.031. |
[4] |
A. Friedman, "Partial Differential Equations of Parabolic Type," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. |
[5] |
V. Isakov, Inverse Parabolic Problems with the final overdetermination, Comm. Pure Appl. Math., 44 (1991), 185-209.
doi: 10.1002/cpa.3160440203. |
[6] |
V. Isakov, "Inverse Problems for Partial Differential Equations," Second Edition, Springer, New York, 2006. |
[7] |
V. Isakov, Some inverse parabolic problems for the diffusion equation, Inverse Problems, 15 (1999), 3-10.
doi: 10.1088/0266-5611/15/1/004. |
[8] |
V. L. Kamynin, On the unique solvability of an inverse problem for parabolic equations under a final overdetermination conditions, Math. Notes, 73 (2003), 202-211.
doi: 10.1023/A:1022107024916. |
[9] |
V. L. Kamynin, On the inverse problem of determining the right-hand side of a parabolic equation under an integral overdetermination conditions, Math. Notes, 77 (2005), 482-493.
doi: 10.1007/s11006-005-0047-6. |
[10] |
O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," AMS, Providence, RI, 1968. |
[11] |
V. Méndez, J. Fort, H. G. Rotstein and S. Fedotov, Speed of reaction-diffusion fronts in spatially heterogeneous media, Phys. Rev. E (3), 68 (2003), 041105.
doi: 10.1103/PhysRevE.68.041105. |
[12] |
C. V. Pao, "Nonlinear Parabolic And Elliptic Equations," Plenum Press, New York, 1992. |
[13] |
A. I. Prilepko and V. V. Solov'ev, Solvability theorems and the Rothe method in inverse problems for an equation of parabolic type II, Diff. Eq., 23 (1987), 1341-1349. |
[14] |
A. B. Kostin and A. I. Prilepko, On certain inverse problems for parabolic equations with final and integral observation, Russian Acad. Sci. Sb. Math., 75 (1993), 473-490.
doi: 10.1070/SM1993v075n02ABEH003394. |
[15] |
H. G. Rotstein, A. M. Zhabotinsky and I. R. Epstein, Dynamics of one- and two-dimensional kinds in bistable reaction-diffusion equations with quasidiscrete sources of reaction, Chaos, 11 (2001), 833-842.
doi: 10.1063/1.1418459. |
show all references
References:
[1] |
M. Choulli, An inverse problem for a semilinear parabolic equation, Inverse Problems, 10 (1994), 1123-1132.
doi: 10.1088/0266-5611/10/5/009. |
[2] |
M. Choulli and M. Yamamoto, An inverse parabolic problem with non-zero initial condition, Inverse Problems, 13 (1997), 19-27.
doi: 10.1088/0266-5611/13/1/003. |
[3] |
M. Choulli and M. Yamamoto, Uniqueness and stability in determining the heat radiative coefficient, the initial temperature and a boundary coefficient in a parabolic equation, Nonlinear Anal., 69 (2008), 3983-3998.
doi: 10.1016/j.na.2007.10.031. |
[4] |
A. Friedman, "Partial Differential Equations of Parabolic Type," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. |
[5] |
V. Isakov, Inverse Parabolic Problems with the final overdetermination, Comm. Pure Appl. Math., 44 (1991), 185-209.
doi: 10.1002/cpa.3160440203. |
[6] |
V. Isakov, "Inverse Problems for Partial Differential Equations," Second Edition, Springer, New York, 2006. |
[7] |
V. Isakov, Some inverse parabolic problems for the diffusion equation, Inverse Problems, 15 (1999), 3-10.
doi: 10.1088/0266-5611/15/1/004. |
[8] |
V. L. Kamynin, On the unique solvability of an inverse problem for parabolic equations under a final overdetermination conditions, Math. Notes, 73 (2003), 202-211.
doi: 10.1023/A:1022107024916. |
[9] |
V. L. Kamynin, On the inverse problem of determining the right-hand side of a parabolic equation under an integral overdetermination conditions, Math. Notes, 77 (2005), 482-493.
doi: 10.1007/s11006-005-0047-6. |
[10] |
O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type," AMS, Providence, RI, 1968. |
[11] |
V. Méndez, J. Fort, H. G. Rotstein and S. Fedotov, Speed of reaction-diffusion fronts in spatially heterogeneous media, Phys. Rev. E (3), 68 (2003), 041105.
doi: 10.1103/PhysRevE.68.041105. |
[12] |
C. V. Pao, "Nonlinear Parabolic And Elliptic Equations," Plenum Press, New York, 1992. |
[13] |
A. I. Prilepko and V. V. Solov'ev, Solvability theorems and the Rothe method in inverse problems for an equation of parabolic type II, Diff. Eq., 23 (1987), 1341-1349. |
[14] |
A. B. Kostin and A. I. Prilepko, On certain inverse problems for parabolic equations with final and integral observation, Russian Acad. Sci. Sb. Math., 75 (1993), 473-490.
doi: 10.1070/SM1993v075n02ABEH003394. |
[15] |
H. G. Rotstein, A. M. Zhabotinsky and I. R. Epstein, Dynamics of one- and two-dimensional kinds in bistable reaction-diffusion equations with quasidiscrete sources of reaction, Chaos, 11 (2001), 833-842.
doi: 10.1063/1.1418459. |
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