Methods for solving inverse problems in mathematical physics prilepko, orlovskiy

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Methods for solving inverse problems in mathematical physics   prilepko, orlovskiy

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Đây là bộ sách tiếng anh về chuyên ngành vật lý gồm các lý thuyết căn bản và lý liên quan đến công nghệ nano ,công nghệ vật liệu ,công nghệ vi điện tử,vật lý bán dẫn. Bộ sách này thích hợp cho những ai đam mê theo đuổi ngành vật lý và muốn tìm hiểu thế giới vũ trụ và hoạt độn ra sao.

[...]... domain 6.5 7 Two-Polnt Inverse Problems for First Order Equations 7.1 Two-point inverse problems 7.2 Inverse problems with self-adjoint operator and scalar function ¯ 7.3 Two-point inverse problems in Banach lattices 8 Inverse 8.1 8.2 8.3 9 Problems for Equations of Second Order Cauchy problem for semilinear hyperbolic equations Two-point inverse problems for equations of hyperbolic type Two-point inverse. .. problems with smoothing overdetermination: quasilinear parabolic equations 6.7 Inverse problems with singular overdetermination: semilinear parabolic equations 6.8 Inverse problems with smoothing overdetermination: semilinear hyperbolic equations 6.9 Inverse problems with singular overdetermination: semilinear hyperbolic equations 6.10 Inverse problems with smoothing overdetermination: semilinear hyperbolic... Preface Inverse 1,1 1,2 1,3 1.4 1.5 2 3 Inverse 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3,9 of Parabolic Type Preliminaries The linear inverse problem: recovering a source term The linear inverse problem: the Fredholm solvability The nonlinear coefficient inverse problem: recovering a coefficient depending on x The linear inverse problem: recovering the evolution of a source term Inverse 2.1 2.2 2.3 Problems for. .. smoothing overdetermination: the basic elements of the theory 6.3 Nonlinear inverse problems ,with smoothing overdetermination: solvability 6.4 Inverse problems with.smoothing overdetermination: smoothness of solution 299 299 329 342 354 364 375 375 380 394 406 xiii Con ~en*s Inverse problems with singular overdetermination: semilinear equations with constant operation in the principal part 6.6 Inverse problems. .. 2.2 2.3 Problems for Equations Problems for Equations of Hyperbolic Type Inverse problems for x-hyperbolic systems Inverse problems for t-hyperbolic systems Inverse problems for hyperbolic equations of the second order Problems for Equations of the Elliptic 54 60 71 71 88 106 Type Introduction to inverse problems in potential theory Necessary and sufficient conditions for the equality of exterior magnetic... Banachspaces Linear differential equations of the second order in Banach spaces Differential equations with varying operator coefficients Boundaryvalue problems for elliptic differential equations of the second order Abstract Inverse Problems for First Order Equations and Their Applications in Mathematical Physics 6.1 Equations of mathematical physics and abstract problems 6.2 The linear inverse problem... density of constant sign Integral equation for finding the density of a given body via its exterior potential Uniqueness of the inverse problem solution for the simple layer potential Stability in inverse problems for the potential of ~, a simple layer in the space R n >_ 3 xi 1 25 41 123 123 127 139 152 166 171 179 192 197 xli 4 Con~en~s Inverse Problems in Dynamics of Viscous Incompressible Fluid 4.1... Pdlepko aL, Methods Solving Inverse Problems Mathematical et for in Physics (2000) Additional Volumes Preparation in Chapter Inverse 1 Problems of Parabolic for Equations Type 1.1 Preliminaries In this section we give the basic notations and notions and present also a number of relevant topics from functional analysis and the general theory of partial differential equations of parabolic type For more... C in the region /) constituting the projection of onto the plane ~,~ = 0 Wewill speak below about the class C~(/)) Weexpoundcertain exploratory devices for investigating inverse problems by using several well-known inequalities In this branch of mathematics common practice involves, for example, the Cauchy inequality E aij i,j=l ~i _ aij ) 1/2 which is valid for an arbitrary nonnegative quadratic form... proven in recent years in connection with the investigation of the series of questions that we now answer Being of independent value although, they are used in the present book only as part of the auxiliary mathematical apparatus The theorems concerned will be formulated here in a common setting capable of describing inverse problems of interest that make it possible to draw fairly accurate outlines . term 1 25 41 54 60 2 Inverse Problems for Equations of Hyperbolic Type 2.1 Inverse problems for x-hyperbolic systems 2.2 Inverse problems for t-hyperbolic systems 2.3 Inverse. 489 7.1 Two-point inverse problems 489 7.2 Inverse problems with self-adjoint operator and scalar function ¯ 501 7.3 Two-point inverse problems in Banach

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