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On the BenilovVynnycky blowup 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 KadomtsevPetviashvili equation and associated constraints, Stud. Appl. Math., 85 (1991), 195213. 
[2] 
E. S. Benilov, On the surface waves in a shallow channel with an uneven bottom, Stud. Appl. Math., 87 (1992), 114. 
[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), 9398. 
[4] 
E. S. Benilov and M. Vynnycky, Contact lines with a $180^{\circ}$ contact angle, J. Fluid Mech., 718 (2013), 481506. 
[5] 
B. B. Kadomtsev and V. I. Petviashvili, On the stability of solitary waves in weakly dispersing media,, Sov. Phys. Dokl., 15 (): 539. 
[6] 
L. A. Ostrovskii, Nonlinear internal waves in the rotating ocean, Okeanologiia, 18 (1978), 181191. 
[7] 
D. E. Pelinovsky and A. R. Giniyatullin, Finitetime singularities in the dynamical evolution of contact lines, Bulletin of the Moscow State Regional University (Physics and Mathematics), 3 (2013), 1424. 
[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), 4560. 
[9] 
D. E. Pelinovsky and C. Xu, On numerical modelling and the blowup behavior of contact lines with a $180^{\circ}$ contact angle, J. Engineer. Math., 2015. doi: 10.1007/s1066501497639. 
[10] 
J. Le Sommer, G. M. Reznik and V. Zeitlin, Nonlinear geostrophic adjustment of longwave disturbances in the shallowwater model on the equatorial betaplane, Journal of Fluid Mechanics, 515 (2004), 135170. doi: 10.1017/S0022112004000229. 
[11] 
M. Vynnycky and S. L. Mitchell, On the accuracy of a finitedifference method for parabolic partial differential equations with discontinuous boundary conditions, Num. Heat Trans B, 64 (2013), 275292. doi: 10.1080/10407790.2013.797312. 
[12] 
S. L. Mitchell and M. Vynnycky, On the numerical solution of twophase Stefan problems with heatflux boundary conditions, J. Comp. Appl. Maths, 264 (2014), 4964. doi: 10.1016/j.cam.2014.01.003. 
show all references
References:
[1] 
M. J. Ablowitz and J. Villarroel, On the KadomtsevPetviashvili equation and associated constraints, Stud. Appl. Math., 85 (1991), 195213. 
[2] 
E. S. Benilov, On the surface waves in a shallow channel with an uneven bottom, Stud. Appl. Math., 87 (1992), 114. 
[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), 9398. 
[4] 
E. S. Benilov and M. Vynnycky, Contact lines with a $180^{\circ}$ contact angle, J. Fluid Mech., 718 (2013), 481506. 
[5] 
B. B. Kadomtsev and V. I. Petviashvili, On the stability of solitary waves in weakly dispersing media,, Sov. Phys. Dokl., 15 (): 539. 
[6] 
L. A. Ostrovskii, Nonlinear internal waves in the rotating ocean, Okeanologiia, 18 (1978), 181191. 
[7] 
D. E. Pelinovsky and A. R. Giniyatullin, Finitetime singularities in the dynamical evolution of contact lines, Bulletin of the Moscow State Regional University (Physics and Mathematics), 3 (2013), 1424. 
[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), 4560. 
[9] 
D. E. Pelinovsky and C. Xu, On numerical modelling and the blowup behavior of contact lines with a $180^{\circ}$ contact angle, J. Engineer. Math., 2015. doi: 10.1007/s1066501497639. 
[10] 
J. Le Sommer, G. M. Reznik and V. Zeitlin, Nonlinear geostrophic adjustment of longwave disturbances in the shallowwater model on the equatorial betaplane, Journal of Fluid Mechanics, 515 (2004), 135170. doi: 10.1017/S0022112004000229. 
[11] 
M. Vynnycky and S. L. Mitchell, On the accuracy of a finitedifference method for parabolic partial differential equations with discontinuous boundary conditions, Num. Heat Trans B, 64 (2013), 275292. doi: 10.1080/10407790.2013.797312. 
[12] 
S. L. Mitchell and M. Vynnycky, On the numerical solution of twophase Stefan problems with heatflux boundary conditions, J. Comp. Appl. Maths, 264 (2014), 4964. doi: 10.1016/j.cam.2014.01.003. 
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