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
Preface | 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 | |
Author Index | 143 |
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Lecture Notes on Mixed Type Partial Differential Equations John Michael Rassias No preview available - 1990 |
Common terms and phrases
a-priori estimate A₁ Akad Assume boundary condition Assume conditions av-K B₁ Bitsadze Bitsadze-Lavrentjev boundary conditions boundary value problems bv₁ C₁ C²(D Cauchy Cauchy Problem Chaplygin equation condition with exponent Consists in finding const curve D₁ D₂ Denote Dokl dxdy dzdy emanating from point energy integral method equa equations of mixed Ext(D F. I. Frankl finding a function Frankl Problem g₁ Gellerstedt Goursat Problem Green's formula Green's theorem Hölder condition hypersurface hypersurfaces S3 In+1 Int(D J. M. Rassias J₁ K(y)uzz Ku² Kv² Math mixed domain Nauk non-characteristic partial differential equations Problem BL Protter quasi-regular solution Riesz representation theorem satisfies a Hölder satisfies equation simply connected solution of Problem tion Tricomi equation Tricomi Problem Un+1 uniqueness v₁ velocity vids weak solution Xn+1 αξ δ₁ θη Κν² ν²