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Sign-changing solutions for fourth order elliptic equations with Kirchhoff-type
Sharp well-posedness for the Chen-Lee equation
1. | Departamento de Matemáticas, Universidad Nacional de Colombia, AK 30 45-03, 111321, Bogotá, Colombia |
2. | Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, RJ, Brazil |
References:
[1] |
B. Alvarez Samaniego, The Cauchy problem for a nonlocal perturbation of the KdV equation, Differential Integral Equations, 16 (2003), 1249-1280. |
[2] |
H. A. Biagioni, J. L. Bona, R. J. Iório Jr. and M. Scialom, On the Korteweg-de Vries-Kuramoto-Sivashinsky equation, Adv. Differential Equations, 1 (1996), 1-20. |
[3] |
J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II. The KdV-equation, Geom. Funct. Anal., 3 (1993), 209-262.
doi: 10.1007/BF01895688. |
[4] |
D. B. Dix, Temporal asymptotic behavior of solutions of the Benjamin-Ono-Burgers equation, J. Differential Equations, 90 (1991), 238-287.
doi: 10.1016/0022-0396(91)90148-3. |
[5] |
D. B. Dix, Nonuniqueness and uniqueness in the initial value problem for Burgers' equation, SIAM J. Math. Anal., 27 (1996), 708-724.
doi: 10.1137/0527038. |
[6] |
O. Duque, Sobre una versión bidimensional de la ecuación Benjamin-Ono generalizada, Ph.D thesis, Universidad Nacional de Colombia, sede Bogotá, 2014. |
[7] |
S. A. Esfahani, High Dimensional Nonlinear Dispersive Models, Ph.D thesis, IMPA, 2008. |
[8] |
B. -F. Feng and T. Kawahara, Temporal evolutions and stationary waves for dissipative Benjamin-Ono equation, Phys. D, 139 (2000), 301-318.
doi: 10.1016/S0167-2789(99)00227-4. |
[9] |
R. J. Iório Jr., On the Cauchy problem for the Benjamin-Ono equation, Comm. Partial Differential Equations, 11 (1986), 1031-1081.
doi: 10.1080/03605308608820456. |
[10] |
C. E. Kenig, G. Ponce and L. Vega, A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc., 9 (1996), 573-603.
doi: 10.1090/S0894-0347-96-00200-7. |
[11] |
Y. C. Lee and H. H. Chen, Nonlinear dynamical models of plasma turbulence, Phys. Scr., T2/1 (1982), 41-47. |
[12] |
R. A. Pastrán, On a Perturbation of the Benjamin-Ono equation, Nonlinear Anal., 93 (2013), 273-296.
doi: 10.1016/j.na.2013.07.014. |
[13] |
R. A. Pastrán and O. G. Riaño, On the well-posedness for the Chen-Lee equation in periodic Sobolev spaces, preprint, Rev. Colombiana Mat., arXiv:1510.00447. |
[14] |
D. Pilod, Sharp well-posedness results for the Kuramoto-Velarde equation, Commun. Pure Appl. Anal., 7 (2008), 867-881.
doi: 10.3934/cpaa.2008.7.867. |
[15] |
S. Qian, H. H. Chen and Y. C. Lee, A turbulence model with stochastic soliton motion, J. Math. Phys., 31 (1990), 506-516.
doi: 10.1063/1.528884. |
[16] |
S. Qian, Y. C. Lee and H. H. Chen, A study of nonlinear dynamical models of plasma turbulence, Phys. Fluids B 1, 1 (1989), 87-98. |
[17] |
S. Vento, Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations, Osaka J. Math., 48 (2011), 933-958. |
show all references
References:
[1] |
B. Alvarez Samaniego, The Cauchy problem for a nonlocal perturbation of the KdV equation, Differential Integral Equations, 16 (2003), 1249-1280. |
[2] |
H. A. Biagioni, J. L. Bona, R. J. Iório Jr. and M. Scialom, On the Korteweg-de Vries-Kuramoto-Sivashinsky equation, Adv. Differential Equations, 1 (1996), 1-20. |
[3] |
J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II. The KdV-equation, Geom. Funct. Anal., 3 (1993), 209-262.
doi: 10.1007/BF01895688. |
[4] |
D. B. Dix, Temporal asymptotic behavior of solutions of the Benjamin-Ono-Burgers equation, J. Differential Equations, 90 (1991), 238-287.
doi: 10.1016/0022-0396(91)90148-3. |
[5] |
D. B. Dix, Nonuniqueness and uniqueness in the initial value problem for Burgers' equation, SIAM J. Math. Anal., 27 (1996), 708-724.
doi: 10.1137/0527038. |
[6] |
O. Duque, Sobre una versión bidimensional de la ecuación Benjamin-Ono generalizada, Ph.D thesis, Universidad Nacional de Colombia, sede Bogotá, 2014. |
[7] |
S. A. Esfahani, High Dimensional Nonlinear Dispersive Models, Ph.D thesis, IMPA, 2008. |
[8] |
B. -F. Feng and T. Kawahara, Temporal evolutions and stationary waves for dissipative Benjamin-Ono equation, Phys. D, 139 (2000), 301-318.
doi: 10.1016/S0167-2789(99)00227-4. |
[9] |
R. J. Iório Jr., On the Cauchy problem for the Benjamin-Ono equation, Comm. Partial Differential Equations, 11 (1986), 1031-1081.
doi: 10.1080/03605308608820456. |
[10] |
C. E. Kenig, G. Ponce and L. Vega, A bilinear estimate with applications to the KdV equation, J. Amer. Math. Soc., 9 (1996), 573-603.
doi: 10.1090/S0894-0347-96-00200-7. |
[11] |
Y. C. Lee and H. H. Chen, Nonlinear dynamical models of plasma turbulence, Phys. Scr., T2/1 (1982), 41-47. |
[12] |
R. A. Pastrán, On a Perturbation of the Benjamin-Ono equation, Nonlinear Anal., 93 (2013), 273-296.
doi: 10.1016/j.na.2013.07.014. |
[13] |
R. A. Pastrán and O. G. Riaño, On the well-posedness for the Chen-Lee equation in periodic Sobolev spaces, preprint, Rev. Colombiana Mat., arXiv:1510.00447. |
[14] |
D. Pilod, Sharp well-posedness results for the Kuramoto-Velarde equation, Commun. Pure Appl. Anal., 7 (2008), 867-881.
doi: 10.3934/cpaa.2008.7.867. |
[15] |
S. Qian, H. H. Chen and Y. C. Lee, A turbulence model with stochastic soliton motion, J. Math. Phys., 31 (1990), 506-516.
doi: 10.1063/1.528884. |
[16] |
S. Qian, Y. C. Lee and H. H. Chen, A study of nonlinear dynamical models of plasma turbulence, Phys. Fluids B 1, 1 (1989), 87-98. |
[17] |
S. Vento, Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations, Osaka J. Math., 48 (2011), 933-958. |
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