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On the Benilov-Vynnycky blow-up problem
1. | Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA 91711, United States |
2. | Department of Mathematical Sciences, Claremont McKenna College, Claremont, CA 91711, United States |
3. | Department of Mathematics, Pitzer College, Claremont, CA 91711, United States |
References:
[1] |
M. J. Ablowitz and J. Villarroel, On the Kadomtsev-Petviashvili equation and associated constraints,, Stud. Appl. Math., 85 (1991), 195.
|
[2] |
E. S. Benilov, On the surface waves in a shallow channel with an uneven bottom,, Stud. Appl. Math., 87 (1992), 1.
|
[3] |
D. J. Benney and W. J. Timson, The rolling motion of a viscous fluid on and off a rigid surface,, Stud. Appl. Math, 63 (1980), 93.
|
[4] |
E. S. Benilov and M. Vynnycky, Contact lines with a $180^{\circ}$ contact angle,, J. Fluid Mech., 718 (2013), 481. Google Scholar |
[5] |
B. B. Kadomtsev and V. I. Petviashvili, On the stability of solitary waves in weakly dispersing media,, Sov. Phys. Dokl., 15 (): 539. Google Scholar |
[6] |
L. A. Ostrovskii, Nonlinear internal waves in the rotating ocean,, Okeanologiia, 18 (1978), 181. Google Scholar |
[7] |
D. E. Pelinovsky and A. R. Giniyatullin, Finite-time singularities in the dynamical evolution of contact lines,, Bulletin of the Moscow State Regional University (Physics and Mathematics), 3 (2013), 14. Google Scholar |
[8] |
D. E. Pelinovsky, A. R. Giniyatullin and Y. A. Panfilova, On solutions of the reduced model for the dynamical evolution of contact lines,, Transactions of Nizhni Novgorod State Technical University n.a. Alexeev N.4, 94 (2012), 45. Google Scholar |
[9] |
D. E. Pelinovsky and C. Xu, On numerical modelling and the blow-up behavior of contact lines with a $180^{\circ}$ contact angle,, J. Engineer. Math., (2015).
doi: 10.1007/s10665-014-9763-9. |
[10] |
J. Le Sommer, G. M. Reznik and V. Zeitlin, Nonlinear geostrophic adjustment of long-wave disturbances in the shallow-water model on the equatorial beta-plane,, Journal of Fluid Mechanics, 515 (2004), 135.
doi: 10.1017/S0022112004000229. |
[11] |
M. Vynnycky and S. L. Mitchell, On the accuracy of a finite-difference method for parabolic partial differential equations with discontinuous boundary conditions,, Num. Heat Trans B, 64 (2013), 275.
doi: 10.1080/10407790.2013.797312. |
[12] |
S. L. Mitchell and M. Vynnycky, On the numerical solution of two-phase Stefan problems with heat-flux boundary conditions,, J. Comp. Appl. Maths, 264 (2014), 49.
doi: 10.1016/j.cam.2014.01.003. |
show all references
References:
[1] |
M. J. Ablowitz and J. Villarroel, On the Kadomtsev-Petviashvili equation and associated constraints,, Stud. Appl. Math., 85 (1991), 195.
|
[2] |
E. S. Benilov, On the surface waves in a shallow channel with an uneven bottom,, Stud. Appl. Math., 87 (1992), 1.
|
[3] |
D. J. Benney and W. J. Timson, The rolling motion of a viscous fluid on and off a rigid surface,, Stud. Appl. Math, 63 (1980), 93.
|
[4] |
E. S. Benilov and M. Vynnycky, Contact lines with a $180^{\circ}$ contact angle,, J. Fluid Mech., 718 (2013), 481. Google Scholar |
[5] |
B. B. Kadomtsev and V. I. Petviashvili, On the stability of solitary waves in weakly dispersing media,, Sov. Phys. Dokl., 15 (): 539. Google Scholar |
[6] |
L. A. Ostrovskii, Nonlinear internal waves in the rotating ocean,, Okeanologiia, 18 (1978), 181. Google Scholar |
[7] |
D. E. Pelinovsky and A. R. Giniyatullin, Finite-time singularities in the dynamical evolution of contact lines,, Bulletin of the Moscow State Regional University (Physics and Mathematics), 3 (2013), 14. Google Scholar |
[8] |
D. E. Pelinovsky, A. R. Giniyatullin and Y. A. Panfilova, On solutions of the reduced model for the dynamical evolution of contact lines,, Transactions of Nizhni Novgorod State Technical University n.a. Alexeev N.4, 94 (2012), 45. Google Scholar |
[9] |
D. E. Pelinovsky and C. Xu, On numerical modelling and the blow-up behavior of contact lines with a $180^{\circ}$ contact angle,, J. Engineer. Math., (2015).
doi: 10.1007/s10665-014-9763-9. |
[10] |
J. Le Sommer, G. M. Reznik and V. Zeitlin, Nonlinear geostrophic adjustment of long-wave disturbances in the shallow-water model on the equatorial beta-plane,, Journal of Fluid Mechanics, 515 (2004), 135.
doi: 10.1017/S0022112004000229. |
[11] |
M. Vynnycky and S. L. Mitchell, On the accuracy of a finite-difference method for parabolic partial differential equations with discontinuous boundary conditions,, Num. Heat Trans B, 64 (2013), 275.
doi: 10.1080/10407790.2013.797312. |
[12] |
S. L. Mitchell and M. Vynnycky, On the numerical solution of two-phase Stefan problems with heat-flux boundary conditions,, J. Comp. Appl. Maths, 264 (2014), 49.
doi: 10.1016/j.cam.2014.01.003. |
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