Adjoint Equations and Perturbation Algorithms in Nonlinear Problems
Adjoint Equations and Perturbation Algorithms in Nonlinear Problems
复制标题
非线性问题中的伴随方程和微扰算法
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
V. Shutyaev
中科院分区：
文献类型：
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作者：
G. Marchuk;V. Agoshkov;V. Shutyaev
非线性问题中伴随算子的构造原理对偶空间与伴随算子基于拉格朗日恒等式的伴随算子的构造基于泰勒公式的伴随算子定义D类算子及其伴随算子的性质基于各种原理构造的伴随算子的性质对应于非线性问题的主算子与伴随算子的一般性质线性算子D类算子的性质用泰勒公式构造的伴随算子的性质非线性问题中主方程和伴随方程的可解性主方程和伴随方程。方程F（u）= y的可解性方程A（u）v = y的可解性方程A（u）v = y的可解性方程A *（u）w = p的可解性方程A *（u）w = p的可解性非线性问题中变换群、守恒律和伴随算子的构造定义。非线性方程和算子。方程的守恒律变换伴随方程不同伴随算子之间的关系用李群和守恒律构造伴随方程的一般说明具有规定性质的伴随算子的构造Noether定理，守恒律与伴随算子伴随方程的若干应用非线性问题的摄动算法原非线性问题的摄动算法线性方程和伴随算子方程基于主方程和伴随方程的非线性泛函的扰动算法扰动算法中的谱方法N阶扰动算法的证明扰动算法的收敛速度估计.拟线性椭圆问题的摄动算法与逐次逼近法的比较伴随方程与迁移理论非线性问题的N阶摄动算法迁移理论的若干问题特征值问题的N阶摄动算法控制问题及其摄动近似解非线性方程的研究与近似解输运方程的线性问题，伴随方程和拟线性运动方程的摄动算法问题的陈述。基本假设。问题的算子公式化变换。非线性算子伴随方程的性质计算泛函的一种算法化学交换过程问题非线性土壤传质数学模型的伴随方程和扰动算法非线性土壤传质数学模型的公式化问题的变换。非线性算子扰动算法的性质。伴随方程有效弥散系数问题的近似解求解伴随方程在科学技术中的应用伴随方程在资料同化问题中的应用伴随方程在流体力学中求解液体边界条件问题的应用形状优化伴随方程方法污染物的全球输运各地区气候变化敏感性问题世界
Principles of Construction of Adjoint Operators in Non-Linear Problems Dual Spaces and Adjoint Operators Construction of Adjoint Operators Based on Using the Lagrange Identity Definition of Adjoint Operators Based on Using Taylor's Formula Operators of the Class D and their Adjoint Operators Properties of Adjoint Operators Constructed on the Basis of Various Principles General Properties of Main and Adjoint Operators Corresponding to Non-Linear Operators Properties of Operators of the Class D Properties of Adjoint Operators Constructed with the Use of the Taylor Formula Solvability of Main and Adjoint Equations in Non-Linear Problems Main and Adjoint Equations. Problems Solvability of the Equation F(u) = y Solvability of the Equation A(u)v = y Solvability of the Equation A(u)v = y Solvability of the Equation A*(u)w = p Solvability of the Equation A*(u)w = p Transformation Groups, Conservation Laws and Construction of the Adjoint Operators in Non-Linear Problems Definitions. Non-Linear Equations and Operators. Conservation Laws Transformation of Equations Adjoint Equations Relationship between Different Adjoint Operators General Remarks on Constructing the Adjoint Equations with the Use of the Lie Groups and Conservation Laws Construction of Adjoint Operators with Prescribed Properties The Noether Theorem, Conservation Laws and Adjoint Operators On Some Applications of Adjoint Equations Perturbation Algorithms in Non-Linear Problems Perturbation Algorithms for Original Non-Linear Equations and Equations Involving Adjoint Operators Perturbation Algorithms for Non-Linear Functionals Based on Using Main and Adjoint Equations Spectral Method in Perturbation Algorithms Justification of the N-th Order Perturbation Algorithms Convergence Rate Estimates for Perturbation Algorithms. Comparison with the Successive Approximation Method Justification of Perturbation Algorithms in Quasi-Linear Elliptic Problems Adjoint Equations and the N-th Order Perturbation Algorithms in Non-Linear Problems of Transport Theory Some Problems of Transport Theory The N-th Order Perturbation Algorithms for an Eigenvalue Problem A Problem of Control and its Approximate Solution with the Use of Perturbation Algorithms Investigation and Approximate Solution of a Non-Linear Problem for the Transport Equation Adjoint Equations and Perturbation Algorithms for a Quasilinear Equation of Motion Statement of the Problem. Basic Assumptions. Operator Formulation Transformation of the Problem. Properties of the Non-Linear Operator Adjoint Equation An Algorithm for Computing the Functional The Problem on Chemical Exchange Processes Adjoint Equations and Perturbation Algorithms for a Non-Linear Mathematical Model of Mass Transfer in Soil Mathematical Models of Mass Transfer in Soil Formulation of a Non-Linear Mathematical Model Transformation of the Problem. Properties of the Non-Linear Operator Perturbation Algorithm. Adjoint Equation Approximate Solution of the Problem on Finding an Effective Dispersion Coefficient An Algorithm for Solving the Problem Applications of Adjoint Equations in Science and Technology Adjoint Equations in Data Assimilation Problems Application of Adjoint Equations for Solving the Problem of Liquid Boundary Conditions in Hydrodynamics Shape Optimization Using Adjoint Equation Approaches Global Transport of Pollutants Problems of Climate Change Sensitivity in Various Regions of the World