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On the solvability conditions for the diffusion equation with convection terms
1. | University of Cape Town, Department of Mathematics, Rondebosch, 7701, South Africa |
2. | Institute of Mathematics, University Lyon 1, 69622 Villeurbann |
References:
[1] |
H. L. Cycon, R. G. Froese, W. Kirsch and B. Simon, "Schrödinger Operators with Application to Quantum Mechanics and Global Geometry," Springer-Verlag, Berlin-Heidelberg-New York, 1987. |
[2] |
A. Ducrot, M. Marion and V. Volpert, "Reaction-diffusion Waves (with the Lewis number different from 1)," Publibook, Paris, 2009. |
[3] |
F. Hamel, H. Berestycki and N. Nadirashvili, Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena, Comm. Math. Phys., 253 (2005), 451-480.
doi: 10.1007/S0022000412019. |
[4] |
F. Hamel, N. Nadirashvili and E. Russ, An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift, C.R. Math. Acad. Sci. Paris, 340 (2005), 347-352.
doi: 10.1016/j.crma.2005.01.012. |
[5] |
B. L. G. Jonsson, M. Merkli, I. M. Sigal and F. Ting, "Applied Analysis," 349 pages (in preparation). |
[6] |
T. Kato, Wave operators and similarity for some non-selfadjoint operators, Math. Ann., 162 (1965/1966), 258-279.
doi: 10.1007/BF01360915. |
[7] |
E. Lieb and M. Loss, "Analysis," Graduate studies in Mathematics, 14, American Mathematical Society, Providence, RI, 1997. |
[8] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics, III. Scattering Theory," Academic Press, 1979. |
[9] |
I. Rodnianski and W. Schlag, Time decay for solutions of Schrödinger equations with rough and time-dependent potentials, Invent. Math., 155 (2004), 451-513.
doi: 10.1007/S0022200303254. |
[10] |
R. Texier-Picard and V. Volpert, Reaction-diffusion-convection problems in unbounded cylinders, Revista Matematica Complutense, 16 (2003), 233-276. |
[11] |
V. Volpert and A. Volpert, Convective instability of reaction fronts. Linear stability analysis, Eur. J. Appl. Math., 9 (1998), 507-525.
doi: 10.1017/S095679259800357X. |
[12] |
A. Volpert and V. Volpert, Fredholm property of elliptic operators in unbounded domains, Trans. Moscow Math. Soc., 67 (2006), 127-197.
doi: 10.1090/S0077155406001592. |
[13] |
V. Vougalter and V. Volpert, Solvability conditions for some non Fredholm operators, Proc. Edinb. Math. Soc., 54 (2011), 249-271.
doi: 10.1017/S0013091509000236. |
[14] |
V. Vougalter and V.Volpert, On the solvability conditions for some non Fredholm operators, Int. J. Pure Appl. Math., 60 (2010), 169-191. |
show all references
References:
[1] |
H. L. Cycon, R. G. Froese, W. Kirsch and B. Simon, "Schrödinger Operators with Application to Quantum Mechanics and Global Geometry," Springer-Verlag, Berlin-Heidelberg-New York, 1987. |
[2] |
A. Ducrot, M. Marion and V. Volpert, "Reaction-diffusion Waves (with the Lewis number different from 1)," Publibook, Paris, 2009. |
[3] |
F. Hamel, H. Berestycki and N. Nadirashvili, Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena, Comm. Math. Phys., 253 (2005), 451-480.
doi: 10.1007/S0022000412019. |
[4] |
F. Hamel, N. Nadirashvili and E. Russ, An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift, C.R. Math. Acad. Sci. Paris, 340 (2005), 347-352.
doi: 10.1016/j.crma.2005.01.012. |
[5] |
B. L. G. Jonsson, M. Merkli, I. M. Sigal and F. Ting, "Applied Analysis," 349 pages (in preparation). |
[6] |
T. Kato, Wave operators and similarity for some non-selfadjoint operators, Math. Ann., 162 (1965/1966), 258-279.
doi: 10.1007/BF01360915. |
[7] |
E. Lieb and M. Loss, "Analysis," Graduate studies in Mathematics, 14, American Mathematical Society, Providence, RI, 1997. |
[8] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics, III. Scattering Theory," Academic Press, 1979. |
[9] |
I. Rodnianski and W. Schlag, Time decay for solutions of Schrödinger equations with rough and time-dependent potentials, Invent. Math., 155 (2004), 451-513.
doi: 10.1007/S0022200303254. |
[10] |
R. Texier-Picard and V. Volpert, Reaction-diffusion-convection problems in unbounded cylinders, Revista Matematica Complutense, 16 (2003), 233-276. |
[11] |
V. Volpert and A. Volpert, Convective instability of reaction fronts. Linear stability analysis, Eur. J. Appl. Math., 9 (1998), 507-525.
doi: 10.1017/S095679259800357X. |
[12] |
A. Volpert and V. Volpert, Fredholm property of elliptic operators in unbounded domains, Trans. Moscow Math. Soc., 67 (2006), 127-197.
doi: 10.1090/S0077155406001592. |
[13] |
V. Vougalter and V. Volpert, Solvability conditions for some non Fredholm operators, Proc. Edinb. Math. Soc., 54 (2011), 249-271.
doi: 10.1017/S0013091509000236. |
[14] |
V. Vougalter and V.Volpert, On the solvability conditions for some non Fredholm operators, Int. J. Pure Appl. Math., 60 (2010), 169-191. |
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