## Lecture Notes on Mixed Type Partial Differential EquationsThis book discusses various parts of the theory of mixed type partial differential equations with boundary conditions such as: Chaplygin's classical dynamical equation of mixed type, the theory of regularity of solutions in the sense of Tricomi, Tricomi's fundamental idea and one-dimensional singular integral equations on non-Carleman type, Gellerstedt's characteristic problem and Frankl's non-characteristic problem, Bitsadze and Lavrentjev's mixed type boundary value problems, quasi-regularity of solutions in the classical sense. Some of the latest results of the author are also presented in this book. |

### Contents

The dynamical equation of mixed type | 1 |

The Tricomi problem | 6 |

Regularity of solutions in the sense of Tricomi | 8 |

Fundamental idea of Tricomi | 9 |

The BitsadzeLavrentjev problem | 33 |

The Gellerstedt problem | 41 |

The Frankl problem | 43 |

Quasiregularity of solutions in the sense of Protter | 54 |

The a b c energy integral method | 55 |

Weak or strong solutions in the classical sense | 86 |

Wellposedness | 123 |

Open problems | 137 |

138 | |

139 | |

143 | |

### Other editions - View all

Lecture Notes on Mixed Type Partial Differential Equations John Michael Rassias No preview available - 1990 |

### Common terms and phrases

a-priori estimate A₁ A₂ Akad Assume boundary condition Assume conditions B₁ B₂ Bitsadze-Lavrentjev boundary conditions boundary value problems bv₁ C₁ Cauchy Cauchy Problem Chaplygin equation Condition C3 condition with exponent Consists in finding const curve cv₂ D₁ D₂ Denote Dokl dzdy emanating from point equa equations of mixed Ext(D F. I. Frankl finding a function Frankl Problem g₁ G₂ Goursat Problem Green's formula Green's theorem Hölder condition hypersurface I₁ Int(D intersecting J. M. Rassias J₁ J₂ K₁ Ku² Kv² Math mixed domain Nauk non-characteristic partial differential equations Problem BL quasi-regular solution R₁ S₁ S₁ US4 satisfies a Hölder satisfies equation simply connected solution of Problem t+x-2tx tion Tricomi equation Tricomi Problem u₁ Un+1 uniqueness v₁ v₁ds v₂ weak solution xn+1