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

Vishal Vasan; Bernard Deconinck

doi:10.3934/dcds.2013.33.3171

Article Contents

2013, Volume 33, Issue 7: 3171-3188. Doi: 10.3934/dcds.2013.33.3171

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

Vishal Vasan^1, and
Bernard Deconinck^2,

1.
Department of Mathematics, Pennsylvania State University, State College, PA, 16802
2.
Department of Applied Mathematics, University of Washington, Campus Box 352420, Seattle, WA 98195

Received: February 29, 2012

Revised: July 31, 2012

Published: June 2013

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Abstract

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.

Keywords:

PDEs with mixed derivatives,
Fokas method.

Mathematics Subject Classification: Primary: 35M33, 35C15; Secondary: 35Q35.

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References

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