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Written by two international experts in the field, this book is the first unified survey of the advances made in the last 15 years on key non-standard and improperly posed problems for partial differential equations.This reference for mathematicians, scientists, and engineers provides an overview of the methodology typically used to study improperly posed problems. It focuses on structural stability--the continuous dependence of solutions on the initial conditions and the modeling equations--and on problems for which data are only prescribed on part of the boundary.The book addresses conti

Differential equations --- Differential equations, Partial --- Approximation theory. --- Improperly posed problems.

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Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.

519.61 --- Numerical methods of algebra --- Differential equations, Partial --- Iterative methods (Mathematics) --- Improperly posed problems. --- Iterative methods (Mathematics). --- Differential equations, Partial -- Improperly posed problems. --- Mathematics. --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Improperly posed problems --- 519.61 Numerical methods of algebra --- Iteration (Mathematics) --- Improperly posed problems in partial differential equations --- Ill-posed problems --- Inkorrekt gestelltes Problem. --- Regularisierungsverfahren. --- Iteration. --- Nichtlineares inverses Problem. --- Numerical analysis --- Iterative Regularization. --- Nonlinear Ill-Posed Problems. --- Nonlinear Inverse Problems.

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Numerical analysis --- Differential equations --- Inverse problems (Differential equations) --- Elasticity --- Problèmes inversés (Equations différentielles) --- Analyse numérique --- Elasticité --- Numerical solutions. --- Mathematical models. --- Solutions numériques --- Modèles mathématiques --- 51 <082.1> --- Mathematics--Series --- Improperly posed problems. --- Mathematical models --- Problèmes inversés (Equations différentielles) --- Analyse numérique --- Elasticité --- Solutions numériques --- Modèles mathématiques --- Elastic properties --- Young's modulus --- Mathematical physics --- Matter --- Statics --- Rheology --- Strains and stresses --- Strength of materials --- Improperly posed problems in numerical analysis --- Numerical solutions --- Improperly posed problems --- Properties --- Ill-posed problems

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Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given to applications of regularization methods as well as to practical methods used in computational analysis.

Monotone operators. --- Differential equations, Partial --- Improperly posed problems. --- Improperly posed problems in partial differential equations --- Operator theory --- Ill-posed problems --- Global analysis (Mathematics). --- Computer science --- Operator theory. --- Functional analysis. --- Mathematical optimization. --- Analysis. --- Computational Mathematics and Numerical Analysis. --- Operator Theory. --- Functional Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematics. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functional analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematics --- Mathematical analysis. --- Analysis (Mathematics). --- Computer mathematics. --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of --- 517.1 Mathematical analysis