A (3+1)-dimensional boundary value problem for equations of Keldysh type (the second kind) is studied. Such problems for equations of Tricomi type (the first kind) or for the wave equation were formulated by M.H. Protter (1954) as multidimensional analogues of Darboux or Cauchy-Goursat plane problems. Now, it is well known that Protter problems are not correctly set, and they have singular generalized solutions, even for smooth right-hand sides. In this paper an analogue of the Protter problem for equations of Keldysh type is given. An appropriate generalized solution with possible singularity is defined. Results for uniqueness and existence of such a generalized solution are obtained. Some a priori estimates are stated.

Zugehörige Institution(en) am KIT |
Fakultät für Mathematik (MATH) |

Publikationstyp |
Zeitschriftenaufsatz |

Jahr |
2017 |

Sprache |
Englisch |

Identifikator |
DOI: 10.1186/s13661-017-0757-1 ISSN: 1687-2762, 1687-2770 KITopen ID: 1000067271 |

Erschienen in |
Boundary value problems |

Band |
2017 |

Heft |
1 |

Seiten |
26 |

Schlagworte |
weakly hyperbolic equations, boundary value problems, generalized solutions, uniqueness, behavior of solution |

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