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偏微分方程中的逆問題-第2版 版權(quán)信息
- ISBN:9787510070235
- 條形碼:9787510070235 ; 978-7-5100-7023-5
- 裝幀:一般膠版紙
- 冊數(shù):暫無
- 重量:暫無
- 所屬分類:>>
偏微分方程中的逆問題-第2版 本書特色
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艾賽科威專著的《偏微分方程中的逆問題(第2版)》were used at several universities.a(chǎn)nd 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……
偏微分方程中的逆問題-第2版 內(nèi)容簡介
本書全面講述了目前偏微分方程中逆問題的理論和數(shù)值方面。逆問題這個(gè)話題十分寬泛,并且得到了眾多科學(xué)家和工程人員的青睞。這是第二版,包括了逆問題領(lǐng)域的*新進(jìn)展,給出了理論和計(jì)算方法,強(qiáng)調(diào)*新觀點(diǎn)和技巧。書中也體現(xiàn)了和**版的不同,做了許多修訂,內(nèi)容更加充實(shí),增加了如偽凸的概念,簡化了證明。新材料的增加反應(yīng)了逆問題理論的*新進(jìn)展。本書對象是偏微分方程及其應(yīng)用領(lǐng)域的數(shù)學(xué)工作者、物理學(xué)家、幾何物理學(xué)家和工程人員。
偏微分方程中的逆問題-第2版 目錄
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.a(chǎn)nd 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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偏微分方程中的逆問題-第2版 作者簡介
Victor Isakov是國際知名學(xué)者,在數(shù)學(xué)和物理學(xué)界享有盛譽(yù)。本書凝聚了作者多年科研和教學(xué)成果,適用于科研工作者、高校教師和研究生。
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