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1 online resource (456 pages) 

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computer c rdamedia 

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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 RiemannHilbert 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 RiemannHilbert problem for elliptic complex equations  1.3 Existence of solutions of discontinuous RiemannHilbert problem for nonlinear complex equations in upper halfunit disk  1.4 The discontinuous RiemannHilbert problem for nonlinear complex equations in general domains  2. The RiemannHilbert Problem for Linear Degenerate Elliptic Complex Equations of First Order  2.1 Formulation of the RiemannHilbert problem for degenerate elliptic complex equations  2.2 Representations and estimates of solutions of RiemannHilbert problem for elliptic complex equations  2.3 Solvability of RiemannHilbert problem for degenerate elliptic complex equations  3. The Discontinuous RiemannHilbert 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 RiemannHilbert problem for elliptic complex equations  3.3 Estimates and existence of solutions of RiemannHilbert problem for degenerate elliptic complex equations  4. The RiemannHilbert Problem for Degenerate Elliptic Complex Equations of First Order in Multiply Connected Domains  4.1 Formulation of RiemannHilbert problem for degenerate elliptic complex equations in multiply connected domains  4.2 Representation and uniqueness of solutions of RiemannHilbert problem for degenerate elliptic complex equations 

4.3 Estimates of solutions of RiemannHilbert problem for degenerate elliptic equations  4.4 Existence of solutions of RiemannHilbert 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 halfunit 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 RiemannHilbert 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 RiemannHilbert problem and uniqueness of its solutions for simplest hyperbolic complex equation  1.3 Uniqueness of solutions of the RiemannHilbert problem for linear hyperbolic complex equations  1.4 Solvability of RiemannHilbert 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 RiemannHilbert 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 RiemannHilbert 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 RiemannHilbert Problem for First Order Complex Equations of Mixed Type  1.1 Formulation of RiemannHilbert problem of complex equations of mixed type  1.2 Representation of RiemannHilbert problem for mixed complex equations  1.3 Unique solvability of RiemannHilbert problem for complex equations of mixed type  2. The RiemannHilbert Problem for First Order Linear Complex Equations of Mixed Type with Parabolic Degeneracy  2.1 Formulation of RiemannHilbert problem for linear degenerate mixed complex equations  2.2 Representation and uniqueness of solutions of RiemannHilbert problem  2.3 Solvability of RiemannHilbert problem for degenerate mixed equations 

3. The Discontinuous RiemannHilbert Problem for First Order Quasilinear Complex Equations of Mixed Type with Degenerate Line  3.1 Representation and uniqueness of solutions of discontinuous RiemannHilbert problem  3.2 RiemannHilbert 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 TricomiRassias 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 

Description based on publisher supplied metadata and other sources 

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 TricomiBers and TricomiFranklRassias 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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