### Abstract

We introduce a method of solving initial boundary value problems for linear evolution equations in a time-dependent domain, and we apply it to an equation with dispersion relation , in the domain [Math Processing Error], [Math Processing Error]. We show that the solution of this problem admits an integral representation in the complex [Math Processing Error] plane, involving either an integral of [Math Processing Error] along a time-dependent contour, or an integral of [Math Processing Error] over a fixed two-dimensional domain. The functions [Math Processing Error] and [Math Processing Error] can be computed through the solution of a system of Volterra linear integral equations. This method can be generalized to nonlinear integrable partial differential equations.

Original language | English |
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Pages (from-to) | 4785-4789 |

Number of pages | 5 |

Journal | Physical Review Letters |

Volume | 84 |

Issue number | 21 |

DOIs | |

Publication status | Published - May 2000 |

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## Cite this

Fokas, A. S., & Pelloni, B. (2000). Method for Solving Moving Boundary Value Problems for Linear Evolution Equations.

*Physical Review Letters*,*84*(21), 4785-4789. https://doi.org/10.1103/PhysRevLett.84.4785