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Well-posedness for degenerate Schrödinger equations
1. | Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato, 5, 40126 Bologna, Italy |
2. | TU Bergakademie Freiberg, Fakultät für Mathematik und Informatik, Institut für Angewandte Analysis, 09596 Freiberg, Germany |
References:
[1] |
A. Ascanelli, M. Cicognani and F. Colombini, The global Cauchy problem for a vibrating beam equation, Journal of Differential Equations, 247 (2009), 1440-1451.
doi: 10.1016/j.jde.2009.06.012. |
[2] |
A. Ascanelli and M. Cicognani, Gevrey solutions for a vibrating beam equation, Rend. Semin. Mat. Torino, 67 (2009), 151-164. |
[3] |
M. Cicognani and F. Colombini, Optimal well-posedness of the cauchy problem for evolution equations with $C^N$ coefficients, Differential and Integral Equations, 17 (2004), 1079-1092. |
[4] |
M. Cicognani and T. Herrmanni, $H^\infty$ well-posedness for a $2$-evolution Cauchy problem with complex coefficients, Journal of Pseudo-Differential Operators and Applications, 4 (2013), 63-90.
doi: 10.1007/s11868-013-0062-4. |
[5] |
S. I. Doi, On the Cauchy problem for Schrödinger type equations and the regularity of solutions, J. Math. Kyoto Univ., 34 (1994), 319-328. |
[6] |
S. I. Doi, Remarks on the Cauchy problem for Schrödingerr-type equations, Comm. Partial Differential Equations, 21 (1996), 163-178.
doi: 10.1080/03605309608821178. |
[7] |
M. Dreher, Necessary conditions for the well-posedness of Schrödinger type equations in Gevrey spaces, Bull. Sci. Math., 127 (2003), 485-503.
doi: 10.1016/S0007-4497(03)00026-5. |
[8] |
W. Ichinose, Some remarks on the Cauchy problem for Schrödinger type equations, Osaka J. Math., 21 (1984), 565-581. |
[9] |
W. Ichinose, Sufficient condition on $H^\infty$ well-posedness for Schrödinger type equations, Comm. Partial Differential Equations, 9 (1984), 33-48.
doi: 10.1080/03605308408820324. |
[10] |
W. Ichinose, On a necessary condition for $L^2$ well-posedness of the Cauchy problem for some Schrödinger type equations with a potential term, J. Math. Kyoto Univ., 33 (1993), 647-663. |
[11] |
W. Ichinose, On the Cauchy problem for Schrödinger type equations and Fourier integral operators, J. Math. Kyoto Univ., 33 (1993), 583-620. |
[12] |
K. Kajitani, The Cauchy problem for Schrödinger type equations with variable coefficients, J. Math. Soc. Japan, 50 (1998), 179-202.
doi: 10.2969/jmsj/05010179. |
[13] |
K. Kajitani and A. Baba, The Cauchy problem for Schrödinger type equations, Bull. Sci. Math., 119 (1995), 459-473. |
[14] |
K. Kajitani and T. Nishitani, The Hyperbolic Cauchy Problem, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1991. |
[15] |
S. Mizohata, On some Schrödinger type equations, Proc. Japan Acad. Ser. A Math. Sci., 57 (1981), 81-84.
doi: 10.3792/pjaa.57.81. |
show all references
References:
[1] |
A. Ascanelli, M. Cicognani and F. Colombini, The global Cauchy problem for a vibrating beam equation, Journal of Differential Equations, 247 (2009), 1440-1451.
doi: 10.1016/j.jde.2009.06.012. |
[2] |
A. Ascanelli and M. Cicognani, Gevrey solutions for a vibrating beam equation, Rend. Semin. Mat. Torino, 67 (2009), 151-164. |
[3] |
M. Cicognani and F. Colombini, Optimal well-posedness of the cauchy problem for evolution equations with $C^N$ coefficients, Differential and Integral Equations, 17 (2004), 1079-1092. |
[4] |
M. Cicognani and T. Herrmanni, $H^\infty$ well-posedness for a $2$-evolution Cauchy problem with complex coefficients, Journal of Pseudo-Differential Operators and Applications, 4 (2013), 63-90.
doi: 10.1007/s11868-013-0062-4. |
[5] |
S. I. Doi, On the Cauchy problem for Schrödinger type equations and the regularity of solutions, J. Math. Kyoto Univ., 34 (1994), 319-328. |
[6] |
S. I. Doi, Remarks on the Cauchy problem for Schrödingerr-type equations, Comm. Partial Differential Equations, 21 (1996), 163-178.
doi: 10.1080/03605309608821178. |
[7] |
M. Dreher, Necessary conditions for the well-posedness of Schrödinger type equations in Gevrey spaces, Bull. Sci. Math., 127 (2003), 485-503.
doi: 10.1016/S0007-4497(03)00026-5. |
[8] |
W. Ichinose, Some remarks on the Cauchy problem for Schrödinger type equations, Osaka J. Math., 21 (1984), 565-581. |
[9] |
W. Ichinose, Sufficient condition on $H^\infty$ well-posedness for Schrödinger type equations, Comm. Partial Differential Equations, 9 (1984), 33-48.
doi: 10.1080/03605308408820324. |
[10] |
W. Ichinose, On a necessary condition for $L^2$ well-posedness of the Cauchy problem for some Schrödinger type equations with a potential term, J. Math. Kyoto Univ., 33 (1993), 647-663. |
[11] |
W. Ichinose, On the Cauchy problem for Schrödinger type equations and Fourier integral operators, J. Math. Kyoto Univ., 33 (1993), 583-620. |
[12] |
K. Kajitani, The Cauchy problem for Schrödinger type equations with variable coefficients, J. Math. Soc. Japan, 50 (1998), 179-202.
doi: 10.2969/jmsj/05010179. |
[13] |
K. Kajitani and A. Baba, The Cauchy problem for Schrödinger type equations, Bull. Sci. Math., 119 (1995), 459-473. |
[14] |
K. Kajitani and T. Nishitani, The Hyperbolic Cauchy Problem, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1991. |
[15] |
S. Mizohata, On some Schrödinger type equations, Proc. Japan Acad. Ser. A Math. Sci., 57 (1981), 81-84.
doi: 10.3792/pjaa.57.81. |
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