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Author Wen, Guo Chun
Title Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy : Including Tricomi-Bers and Tricomi-Frankl-Rassias Problems
Imprint Singapore : World Scientific Publishing Co Pte Ltd, 2007
©2007
book jacket
Descript 1 online resource (456 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Peking University Series in Mathematics Ser. ; v.4
Peking University Series in Mathematics Ser
Note Intro -- Contents -- Preface -- Chapter I Elliptic Complex Equations of First Order -- 1. The Discontinuous Riemann-Hilbert Problem for Nonlinear Uniformly Elliptic Complex Equations of First Order -- 1.1 Reduction of general uniformly elliptic systems of rst order equations to standard complex form -- 1.2 Representation of solutions of discontinuous Riemann-Hilbert problem for elliptic complex equations -- 1.3 Existence of solutions of discontinuous Riemann-Hilbert problem for nonlinear complex equations in upper half-unit disk -- 1.4 The discontinuous Riemann-Hilbert problem for nonlinear complex equations in general domains -- 2. The Riemann-Hilbert Problem for Linear Degenerate Elliptic Complex Equations of First Order -- 2.1 Formulation of the Riemann-Hilbert problem for degenerate elliptic complex equations -- 2.2 Representations and estimates of solutions of Riemann-Hilbert problem for elliptic complex equations -- 2.3 Solvability of Riemann-Hilbert problem for degenerate elliptic complex equations -- 3. The Discontinuous Riemann-Hilbert Problem for Quasilinear Degenerate Elliptic Complex Equations of First Order -- 3.1 Formulation of discontinuous Riemann- Hilbert problem for degenerate elliptic complex equations -- 3.2 Representation and uniqueness of solutions of discontinuous Riemann-Hilbert problem for elliptic complex equations -- 3.3 Estimates and existence of solutions of Riemann-Hilbert problem for degenerate elliptic complex equations -- 4. The Riemann-Hilbert Problem for Degenerate Elliptic Complex Equations of First Order in Multiply Connected Domains -- 4.1 Formulation of Riemann-Hilbert problem for degenerate elliptic complex equations in multiply connected domains -- 4.2 Representation and uniqueness of solutions of Riemann-Hilbert problem for degenerate elliptic complex equations
4.3 Estimates of solutions of Riemann-Hilbert problem for degenerate elliptic equations -- 4.4 Existence of solutions of Riemann-Hilbert problem for degenerate elliptic equations -- Chapter II Elliptic Complex Equations of Second Order -- 1. The Discontinuous Oblique Derivative Problem for Uniformly Elliptic Complex Equations -- 1.1 Formulation of discontinuous oblique derivative problem for elliptic equations -- 1.2 The representation theorem of discontinuous oblique derivative problem for elliptic equations -- 1.3 Existence of solutions of discontinuous oblique derivative problem for elliptic equations in upper half-unit disk -- 1.4 The discontinuous oblique derivative problem for elliptic equations in general domains -- 2. The Mixed Boundary Value Problem for Degenerate Elliptic Equations of Second Order -- 2.1 Formulation of mixed boundary value problem for degenerate elliptic equations of second order -- 2.2 Representation of solutions of mixed boundary value problem for degenerate elliptic equations -- 2.3 Estimates and existence of solutions of mixed problem for degenerate elliptic equations -- 3. The Oblique Derivative Problem for Second Order Elliptic Equations with Nonsmooth Degenerate Line -- 3.1 Formulation of oblique derivative problem for degenerate elliptic equations -- 3.2 Representation of solutions of oblique derivative problem for elliptic equations -- 3.3 Estimates of solutions of oblique derivative problem for elliptic equations -- 3.4 Existence of solutions of oblique derivative problem for elliptic equations -- 4. Boundary Value Problems for Homogeneous Elliptic Equations of Second Order with Degenerate Rank 0 -- 4.1 Boundary value problems for homogeneous elliptic equations of second order with degenerate rank 0 -- 4.2 Boundary value problems for axisymmetric ltration
5. The Oblique Derivative Problem for Nonhomogeneous Elliptic Equations of Second Order with Degenerate Rank 0 -- 5.1 Formulation of oblique derivative problems for degenerate elliptic equations -- 5.2 Representation of solutions of oblique derivative problem of elliptic equations -- 5.3 Estimates and existence of solutions of oblique derivative derivative problems -- Chapter III Hyperbolic Complex Equations of First and Second Orders -- 1. The Riemann-Hilbert Problem for Uniformly Hyperbolic Complex Equations of First Orde -- 1.1 Complex forms of linear and quasilinear hyperbolic system of rst order equations -- 1.2 Formulation of the Riemann-Hilbert problem and uniqueness of its solutions for simplest hyperbolic complex equation -- 1.3 Uniqueness of solutions of the Riemann-Hilbert problem for linear hyperbolic complex equations -- 1.4 Solvability of Riemann-Hilbert problem for linear hyperbolic complex equations -- 1.5 Another boundary value problem for linear hyperbolic complex equations of rst order -- 2. Boundary Value Problems for Degenerate Hyperbolic Complex Equations of First Order . -- 2.1 Formulation of Riemann-Hilbert problem for degenerate hyperbolic complex equations of rst order -- 2.2 Representation of solutions of Riemann- Hilbert problem for degenerate hyperbolic complex equations -- 2.3 Existence and uniqueness of solutions of Riemann-Hilbert problem -- 2.4 Unique solvability of Cauchy problem for degenerate hyperbolic complex equations -- 3. The Oblique Derivative Problem for Uniformly Hyperbolic Equations of Second Order -- 3.1 Complex forms of hyperbolic equations of second order -- 3.2 Formulation of oblique derivative problem and representations of solutions -- 3.3 Existence and uniqueness of solutions of oblique derivative problems -- 4. The Oblique Derivative Problem for Degenerate Hyperbolic Equations of Second Order
4.1 Formulation of discontinuous oblique derivative problem for degenerate hyperbolic equations -- 4.2 Representation and solvability of oblique derivative problem for degenerate hyperbolic equations -- 4.3 Oblique derivative problem for degenerate hyperbolic equations in general domains -- 5. The Oblique Derivative Problem for Second Order Hyperbolic Equations with Degenerate Rank 0 -- 5.1 Formulation of oblique derivative problem for second order hyperbolic equations -- 5.2 Representations of solutions of oblique derivative problems for second order hyperbolic equations -- 5.3 Unique solvability of oblique derivative problem for second order hyperbolic equations -- 5.4 Oblique derivative problems for quasilinear hyperbolic equations with degenerate rank 0 -- 6. The Cauchy Problem for Hyperbolic Equations of Second Order with Degenerate Rank 0 -- 6.1 Formulation of Cauchy problem for second order hyperbolic equations -- 6.2 Reduction of Cauchy problem for degenerate hyperbolic equations to integral equations -- 6.3 Existence of solutions of Cauchy problem for degenerate hyperbolic equations -- Chapter IV First Order Complex Equations of Mixed Type -- 1. The Riemann-Hilbert Problem for First Order Complex Equations of Mixed Type -- 1.1 Formulation of Riemann-Hilbert problem of complex equations of mixed type -- 1.2 Representation of Riemann-Hilbert problem for mixed complex equations -- 1.3 Unique solvability of Riemann-Hilbert problem for complex equations of mixed type -- 2. The Riemann-Hilbert Problem for First Order Linear Complex Equations of Mixed Type with Parabolic Degeneracy -- 2.1 Formulation of Riemann-Hilbert problem for linear degenerate mixed complex equations -- 2.2 Representation and uniqueness of solutions of Riemann-Hilbert problem -- 2.3 Solvability of Riemann-Hilbert problem for degenerate mixed equations
3. The Discontinuous Riemann-Hilbert Problem for First Order Quasilinear Complex Equations of Mixed Type with Degenerate Line -- 3.1 Representation and uniqueness of solutions of discontinuous Riemann-Hilbert problem -- 3.2 Riemann-Hilbert problem for quasilinear mixed equations in general domains -- 4. The General Boundary Value Problem for Quasilinear Mixed Complex Equations with Degenerate Line -- 4.1 Formulation of general boundary value problem for complex equations of mixed type -- 4.2 Representation of solutions for general boundary value problem -- 4.3 Solvability of general boundary value problem for degenerate mixed equations -- Chapter V Second Order Linear Equations of Mixed Type -- 1. The Oblique Derivative Problem for Second Order Equations of Uniformly Mixed Type -- 1.1 Formulation of oblique derivative problem for second order equations of mixed type -- 1.2 Representation and uniqueness of solutions for oblique derivative problem -- 1.3 The solvability of oblique derivative problem for second order equations of mixed type -- 2. The Tricomi Problem for Second Order Degenerate Equations of Mixed Type -- 2.1 The Tricomi problem of second order degenerate equations of mixed type -- 2.2 Representation and uniqueness of solutions of Tricomi problem for degenerate mixed equations -- 2.3 Existence of solutions of Tricomi problem for degenerate equations of mixed type -- 3. The Discontinuous Oblique Derivative Problem for Second Order Degenerate Equations of Mixed Type -- 3.1 Formulation of discontinuous oblique derivative problem for equations of mixed type -- 3.2 Representation of solutions of discontinuous oblique derivative problem for mixed equations -- 3.3 Solvability of discontinuous oblique derivative problem for degenerate equations of mixed type
4. The Exterior Tricomi-Rassias Problem for Second Order Degenerate Equations of Mixed Type
Key Features:Contains an original, detailed presentation of complex analytic methods to solve many problems regarding elliptic, hyperbolic and mixed complex equations with degenerate linesServes as a valuable resource for researchers to solve problems of practical interest in the applications of gas dynamics
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Wen, Guo Chun Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy : Including Tricomi-Bers and Tricomi-Frankl-Rassias Problems Singapore : World Scientific Publishing Co Pte Ltd,c2007 9789812779427
Subject Differential equations, Elliptic.;Differential equations, Hyperbolic.;Differential equations, Partial.;Boundary value problems
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