偏微分方程中的逆问题-第2版

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作者：VictorIsakov[著]

出版社：世界图书出版公司

本类榜单：自然科学

分类：自然科学 > 数学 > 微积分

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ISBN：9787510070235
装帧：一般胶版纸
册数：暂无
重量：暂无
开本：24开
页数：344
出版时间：2014-03-01
条形码：9787510070235 ; 978-7-5100-7023-5

本书特色

in 8 years after publication of the first version of this book，the rapidly progressing field of inverse problems witnessed changes and new developments parts of艾赛科威专著的《偏微分方程中的逆问题(第2版)》were used at several universities．and many colleagues and students as well asmyselfobserved several misprintsandimprecisions some ofthe research problems from the first edition have been solved this edition serves the purposes of reflecting these changes and making appropiate corrections 1 hope that these additions and corrections resulted in not too many new errors and misprints chapters i and 2 contain only 2-3 pages of new materiaijike in sections 1．5． 2 5 chapter 3 order equations and included bound……

内容简介

本书全面讲述了目前偏微分方程中逆问题的理论和数值方面。逆问题这个话题十分宽泛，并且得到了众多科学家和工程人员的青睐。这是第二版，包括了逆问题领域的*新进展，给出了理论和计算方法，强调*新观点和技巧。书中也体现了和**版的不同，做了许多修订，内容更加充实，增加了如伪凸的概念，简化了证明。新材料的增加反应了逆问题理论的*新进展。本书对象是偏微分方程及其应用领域的数学工作者、物理学家、几何物理学家和工程人员。

prefaee to the second edition
prefacetothefirstedifion
chapter l inverse problems
    1．1 the inverse problem of gravimetry
    1．2 the lnverse conductivity problem
    1．3 inverse scattering
    1．4 tomography and the inverse seismic problem
    1．5 inverse spectral problems
chapter 2 ill-posed problems and regularization
    2．1 well．and ill—posed problems
    2．2 conditional correctness：regularization
    2．3 construetion of regularizers
    2．4 convergence of regularization algorithms
    2．5 herative algorithms
chapter 3 uniqueness and stability in the cauchy problem
    3．1 the backward parabolic equation
    3．2 general carleman estimates and the cauchy problem
    3．3 elliptic and parabolic equations
    3．4 hyperbolic and schr6dinger equations
    3．5 systems of partial differential equations
    3．6 open problems
chapter 4 elliptic equations：single boundary measurements
    4．0 results on elliptic boundary value problems
    4．1 inverse gravimetry
    4．2 reconstruction of lowcr-order terms
    4．3 the jbvefsc conductivity problem
    4．4 methods of the theory of one complex variable
    4．5 linearization of the coe佑cients problem
    4．6 some problems ofdetection ofdefects
    4．7 open problems
chapter 5 elliptic equations：many boundary measurements
    5．o the dirichlet．to—neumann map
    5．1 boundary reconstruction
    5．2 reconstruction in q
    5．3 completeness of products of solutions of pde
    5．4 recovery of several coeffcients
    5．5 the plane case
    5．6 nonlinear equations
    5．7 discontinuous conductivities
    5．8 maxwell’s and elasticity systems
    5．9 open problems
chapter 6 scattering problems
    6．0 direct scattering
    6 l from a to nearfield
    6 2 scattering by a medium
    6．3 scattering by obstacles
    6．4 open problems
chapter 7 integral geometry and tomography
    7．1 the radon transfofin and its inverse
    7．2 the energy integral methods
    7 3 boman’s counterexample
    7．4 the transport equation
    7．5 open problems
chapter 8 hyperbolic problems
    8．0 introduction
    8．1 the one．dimensional case
    8．2 single boundary measurements
    8．3 many measurements：use of beam solutions
    8．4 many measurements：methods of boundary control
    8．5 recovery ofdiscontinuity ofthe speed ofpropagation
    8．6 open problems
chapter 9 inverse parabolic problems
    9．0 introduction
    9．1 final orerdetermination
    9．2 lateral orerdetermination：single measurements
    9．3 ne inverse problem of option pricing
    9．4 lateral overdetermination：many measurements
    9．5 discontinuous principal coemcient and recovery of a domain
    9．6 nonlinear equations
    9．7 interior sources
    9．8 open problems
chapter 10 some numerical methods
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