非线性复分析及其应用
1970-1
科学出版社
闻国椿
447
The book is a continuation of development of" Boundary value problems for nonlinear elliptic equations and systems" and "Linear and quasilinear equations of hyperbolic and mixed types ".A large portion of the work is devoted to boundary value problems for general elliptic complex equations of first,second and fourth order,initial-boundary value problems for nonlinear parabolic complex equations of first and second order.Moreover,some results about first and second order complex equations of mixed (elliptic-hyperbolic) type are investigated .Applications of nonlinear complex analysis to continuum mechanics are also introduced.
PrefaceChapter 1 Nonlinear Elliptic Complex Equations of First Order 1.1 Discontinuous Riemann-Hilbert Problem for Nonlinear Uniformly Elliptic Complex Equations of First Order 1.2 Boundary Value Problems for Elliptic Complex Equations with Nonsmooth Boundary 1.3 Nonlinear Riemann-Hilbert Problem for Elliptic Complex Equations in Multiply Connected Domains 1.4 The Riemann-Hilbert Problem for Quasilinear Degenerate Elliptic Complex Equations of First Order 1.5 Discontinuous Riemann-Hilbert Problem for Quasilinear Degenerate Elliptic Complex Equations of First OrderChapter 2 Nonlinear Elliptic Equations of Second Order 2.1 Discontinuous Oblique Derivative Problem for Uniformly Elliptic Complex Equations of Second Order 2.2 Poincare Boundary Value Problem for Nonlinear Elliptic Equations of Second Order 2.3 General Oblique Derivative Problem for Nonlinear Elliptic Equations of Second Order 2.4 Discontinuous Irregular Oblique Derivative Problem of Nonlinear Elliptic Equations of Second Order 2.5 Boundary Value Problems for Nonlinear Degenerate Elliptic Equations of Second OrderChapter 3 Nonlinear Elliptic Systems of Equations 3.1 Boundary Value Problems for Uniformly Elliptic Systems of Second Order Equations 3.2 Boundary Value Problems for Nonlinear Elliptic Systems of Second Order Equations 3.3 Boundary Value Problems of Nonlinear Elliptic Systems of Several First Order Complex Equations 3.4 Boundary Value Problems for Nonlinear Elliptic Systems with Several Unknown Functions 3.5 Degenerate Elliptic Systems of Second Order with Several Unknown Functions 3.6 Boundary Value Problems for Nonlinear Elliptic Complex Equations Second Order 5.3 Oblique Derivative Problem for Quasilinear Degenerate Hyperbolic Equations of Second Order 5.4 Cauchy Problem for Quasilinear Hyperbolic Equations with Degenerate Rank 0 5.5 Darboux Type Problem for Degenerate Hyperbolic Systems of Second Order EquationsChapter 6 Quasilinear Equations of Mixed Type 6.1 The Riemann-Hilbert Problem for First Order Complex Equations of Mixed Type with Degenerate Line 6.2 The Tricomi Problem for Second Order Quasilinear Equations of Mixed Type with Parabolic Degeneracy 6.3 Frankl Type Problem for Second Order Quasilinear Degenerate Equations of Mixed Type 6.4 Boundary Value Problems for Degenerate Equations of Mixed Type in Multiply Connected Domains 6.5 Oblique Derivative Problem for Quasilinear Equations of Mixed Type with Nonsmooth Degenerate Line 6.6 Oblique Derivative Problem for Second Order Quasilinear Systems of Mixed Type with Parabolic DegeneracyChapter 7 Applications of Nonlinear Complex Analysis to Continuum Mechanics 7.1 Free Boundary Problems in Planar Filtration 7.2 Degenerate Elliptic Boundary Value Problem and Axisymmetric Filtration 7.3 Some Free Boundary Problems in Planar Subsonic Flow 7.4 Free Boundary Problems for Cavity Flows in Gas Dynamics 7.5 Free Boundary Problems in Elastico-Plastic MechanicsReferences
