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Well-posedness of boundary-value problems for the linear Benjamin-Bona-Mahony equation

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  • A new method due to Fokas for explicitly solving boundary-value problems for linear partial differential equations is extended to equations with mixed partial derivatives. The Benjamin-Bona-Mahony equation is used as an example: we consider the Robin problem for this equation posed both on the half line and on the finite interval. For specific cases of the Robin boundary conditions the boundary-value problem is found to be ill posed.
    Mathematics Subject Classification: Primary: 35M33, 35C15; Secondary: 35Q35.


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