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Nanking Massacre, Nanjing, Jiangsu Sheng, China, 1937 --- J3386.20 --- J4850 --- S04/0825 --- S07/0200 --- Nan-ching ta tʻu sha, Nanjing, Jiangsu Sheng, China, 1937 --- Nanjing da tu sha, Nanjing, Jiangsu Sheng, China, 1937 --- Nanking Massacre, Nan-ching shih, China, 1937 --- Rape of Nanking, Nanjing, Jiangsu Sheng, China, 1937 --- Massacres --- Sino-Japanese War, 1937-1945 --- Nanjing, Battle of, Nanjing, Jiangsu Sheng, China, 1937 --- Japan: History -- Gendai, modern -- Shōwa period -- World War II -- war with China -- Nanking massacre (1937) --- Japan: International law -- law of peace and war (including war crimes) --- China: History--War against Japan: 1931/1937 - 1945 --- China: Army and police force--Military history --- Atrocities --- Nanjing (Jiangsu Sheng, China) --- History. --- Nanking Massacre, Nanjing, Jiangsu Sheng, China, 1937.

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This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions. The formulation is different from that of Dirichlet-to-Neumann maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. These types of inverse problems include coefficient inverse problems of determining physical parameters in inhomogeneous media that appear in many applications related to electromagnetism, elasticity, and related phenomena. Although the methodology was created in 1981 by Bukhgeim and Klibanov, its comprehensive development has been accomplished only recently. In spite of the wide applicability of the method, there are few monographs focusing on combined accounts of Carleman estimates and applications to inverse problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates, the theory of which has been established within a very general framework, so that the method using Carleman estimates for inverse problems is misunderstood as being very difficult. The main purpose of the book is to provide an accessible approach to the methodology. To accomplish that goal, the authors include a direct derivation of Carleman estimates, the derivation being based essentially on elementary calculus working flexibly for various equations. Because the inverse problem depends heavily on respective equations, too general and abstract an approach may not be balanced. Thus a direct and concrete means was chosen not only because it is friendly to readers but also is much more relevant. By practical necessity, there is surely a wide range of inverse problems and the method delineated here can solve them. The intention is for readers to learn that method and then apply it to solving new inverse problems.

Mathematics. --- Functional analysis. --- Partial differential equations. --- Differential geometry. --- Manifolds (Mathematics). --- Complex manifolds. --- Mathematical physics. --- Partial Differential Equations. --- Functional Analysis. --- Differential Geometry. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Mathematical Physics. --- Inverse problems (Differential equations) --- Differential equations --- Differential equations, partial. --- Global differential geometry. --- Cell aggregation --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Geometry, Differential --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Partial differential equations --- Physical mathematics --- Physics --- Analytic spaces --- Manifolds (Mathematics) --- Topology --- Differential geometry --- Mathematics

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This volume contains 13 chapters, which are extended versions of the presentations at International Conference on Inverse Problems at Fudan University, Shanghai, China, October 12-14, 2018, in honor of Masahiro Yamamoto on the occasion of his 60th anniversary. The chapters are authored by world-renowned researchers and rising young talents, and are updated accounts of various aspects of the researches on inverse problems. The volume covers theories of inverse problems for partial differential equations, regularization methods, and related topics from control theory. This book addresses a wide audience of researchers and young post-docs and graduate students who are interested in mathematical sciences as well as mathematics.

Partial differential equations. --- Functional analysis. --- Integral equations. --- Partial Differential Equations. --- Functional Analysis. --- Integral Equations. --- Partial differential operators. --- Differential operators --- Equations, Integral --- Functional equations --- Functional analysis --- Functional calculus --- Calculus of variations --- Integral equations --- Partial differential equations