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Well-posedness of boundary-value problems for the linear Benjamin-Bona-Mahony equation
1. | Department of Mathematics, Pennsylvania State University, State College, PA, 16802, United States |
2. | Department of Applied Mathematics, University of Washington, Campus Box 352420, Seattle, WA 98195 |
References:
[1] |
A. S. Fokas, "A Unified Approach to Boundary Value Problems,", SIAM: CBMS-NSF Regional Conference Series in Applied Mathematics, (2008).
doi: 10.1137/1.9780898717068. |
[2] |
B. Deconinck, T. Trogdon and V. Vasan, The method of Fokas for solving linear partial differential equations,, Accepted for publication (SIAM Review), (2012), 1. Google Scholar |
[3] |
A. S. Fokas, Boundary-value problems for linear PDEs with variable coefficients,, Proc. R. Soc. Lond, 460 (2004), 1131.
doi: 10.1098/rspa.2003.1208. |
[4] |
P. A. Treharne and A. S. Fokas, Initial-boundary value problems for linear PDEs with variable coefficients,, Math. Proc. Camb. Phil. Soc., 143 (2007), 221.
doi: 10.1017/S0305004107000084. |
[5] |
P. A. Treharne and A. S. Fokas, Boundary value problems for systems of linear evolution equations,, IMA J. Applied Math., 69 (2004), 539.
doi: 10.1093/imamat/69.6.539. |
[6] |
A. S. Fokas and B. Pelloni, Generalized Dirichlet to Neumann Map for moving boundary value problems,, J. Math. Phys., 48 (2007).
doi: 10.1063/1.2405405. |
[7] |
K. Kalimeris and A. S. Fokas, The heat equation in the interior of an equilateral triangle,, Studies in Applied Math., 124 (2010), 283.
doi: 10.1111/j.1467-9590.2009.00471.x. |
[8] |
S. A. Smitheman, E. A. Spence and A. S. Fokas, A spectral collocation method for the Laplace and modified Helmholtz equations in a convex polygon,, IMA J. Num. Anal., 30 (2010), 1184.
doi: 10.1093/imanum/drn079. |
[9] |
T. B. Benjamin, J. L. Bona and J. J. Mahony, Model equations for long waves in nonlinear dispersive systems,, Phil. Trans. Roy. Soc. London. Ser. A, 272 (1972), 47.
|
[10] |
A. S. Fokas, On a class of physically important integrable equations,, Physica D, 87 (1995), 145.
doi: 10.1016/0167-2789(95)00133-O. |
[11] |
A. S. Fokas and B. Pelloni, Boundary value problems for Boussinesq type systems,, Math. Phys. Anal. Geom., 8 (2005), 59.
doi: 10.1007/s11040-004-1650-6. |
[12] |
J. M.-K. Hong, J. Wu and J.-M. Yuan, A new solution representation for the BBM equation in a quarter plane and the eventual periodicity,, Nonlinearity, 22 (2009), 1927.
doi: 10.1088/0951-7715/22/8/009. |
[13] |
J. L. Bona and P. J. Bryant, A mathematical model for long waves generated by wavemakers in non-linear dispersive systems,, Proc. Camb. Phil. Soc., 73 (1973), 391.
|
show all references
References:
[1] |
A. S. Fokas, "A Unified Approach to Boundary Value Problems,", SIAM: CBMS-NSF Regional Conference Series in Applied Mathematics, (2008).
doi: 10.1137/1.9780898717068. |
[2] |
B. Deconinck, T. Trogdon and V. Vasan, The method of Fokas for solving linear partial differential equations,, Accepted for publication (SIAM Review), (2012), 1. Google Scholar |
[3] |
A. S. Fokas, Boundary-value problems for linear PDEs with variable coefficients,, Proc. R. Soc. Lond, 460 (2004), 1131.
doi: 10.1098/rspa.2003.1208. |
[4] |
P. A. Treharne and A. S. Fokas, Initial-boundary value problems for linear PDEs with variable coefficients,, Math. Proc. Camb. Phil. Soc., 143 (2007), 221.
doi: 10.1017/S0305004107000084. |
[5] |
P. A. Treharne and A. S. Fokas, Boundary value problems for systems of linear evolution equations,, IMA J. Applied Math., 69 (2004), 539.
doi: 10.1093/imamat/69.6.539. |
[6] |
A. S. Fokas and B. Pelloni, Generalized Dirichlet to Neumann Map for moving boundary value problems,, J. Math. Phys., 48 (2007).
doi: 10.1063/1.2405405. |
[7] |
K. Kalimeris and A. S. Fokas, The heat equation in the interior of an equilateral triangle,, Studies in Applied Math., 124 (2010), 283.
doi: 10.1111/j.1467-9590.2009.00471.x. |
[8] |
S. A. Smitheman, E. A. Spence and A. S. Fokas, A spectral collocation method for the Laplace and modified Helmholtz equations in a convex polygon,, IMA J. Num. Anal., 30 (2010), 1184.
doi: 10.1093/imanum/drn079. |
[9] |
T. B. Benjamin, J. L. Bona and J. J. Mahony, Model equations for long waves in nonlinear dispersive systems,, Phil. Trans. Roy. Soc. London. Ser. A, 272 (1972), 47.
|
[10] |
A. S. Fokas, On a class of physically important integrable equations,, Physica D, 87 (1995), 145.
doi: 10.1016/0167-2789(95)00133-O. |
[11] |
A. S. Fokas and B. Pelloni, Boundary value problems for Boussinesq type systems,, Math. Phys. Anal. Geom., 8 (2005), 59.
doi: 10.1007/s11040-004-1650-6. |
[12] |
J. M.-K. Hong, J. Wu and J.-M. Yuan, A new solution representation for the BBM equation in a quarter plane and the eventual periodicity,, Nonlinearity, 22 (2009), 1927.
doi: 10.1088/0951-7715/22/8/009. |
[13] |
J. L. Bona and P. J. Bryant, A mathematical model for long waves generated by wavemakers in non-linear dispersive systems,, Proc. Camb. Phil. Soc., 73 (1973), 391.
|
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