Wei Chen

Tatsien Li

Yongji Tan

Zhijie Cai

Jingnong Wang

Spontaneous potential (SP) well-logging is one of the most common and useful well-logging techniques in petroleum exploitation. This monograph is the first of its kind on the mathematical model of spontaneous potential well-logging and its numerical solutions. The mathematical model established in this book shows the necessity of introducing Sobolev spaces with fractional power, which seriously increases the difficulty of proving the well-posedness and proposing numerical solution schemes. In this book, in the axisymmetric situation the well-posedness of the corresponding mathematical model is proved and three efficient schemes of numerical solution are proposed, supported by a number of numerical examples to meet practical computation needs.

Mathematical Model of Spontaneous Potential Well-Logging and Its Numerical Solutions

Philippe G. Ciarlet

Yvon Maday

This book collects papers mainly presented at the "International Conference on Partial Differential Equations: Theory, Control and Approximation" (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions. The contributors are leading experts from all over the world, including members of the Academies of Sciences in France, the USA and China etc., and their papers cover key fields of research, e.g. partial differential equations, control theory and numerical analysis, that Jacques-Louis Lions created or contributed so much to establishing.

In Honor of the Scientific Heritage of Jacques-Louis Lions

Partial Differential Equations: Theory, Control and Approximation

Jean-michel Coron

Yachun Li

This book is a collection of lecture notes for the LIASFMA Shanghai Summer School on 'One-dimensional Hyperbolic Conservation Laws and Their Applications' which was held during August 16 to August 27, 2015 at Shanghai Jiao Tong University, Shanghai, China. This summer school is one of the activities promoted by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA in short). LIASFMA was established jointly by eight institutions in China and France in 2014, which is aimed at providing a platform for some of the leading French and Chinese mathematicians to conduct in-depth researches, extensive exchanges, and student training in the field of applied mathematics. This summer school has the privilege of being the first summer school of the newly established LIASFMA, which makes it significant.

One-dimensional Hyperbolic Conservation Laws And Their Applications

Weiping Zhang

Molin Ge

Jiaxing Hong

This book is a collection of papers in memory of Gu Chaohao on the subjects of Differential Geometry, Partial Differential Equations and Mathematical Physics that Gu Chaohao made great contributions to with all his intelligence during his lifetime. All contributors to this book are close friends, colleagues and students of Gu Chaohao. They are all excellent experts among whom there are 9 members of the Chinese Academy of Sciences. Therefore this book will provide some important information on the frontiers of the related subjects. Contents:A Profile of the Late Professor Gu Chaohao (Tatsien Li)List of Publications of Gu ChaohaoIn Memory of Professor Gu Chaohao (Xiaqi Ding)In Memory of Professor Gu Chaohao (Gongqing Zhang (Kung-Ching Chang))Stability of E-H Mach Configuration in Pseudo-Steady Compressible Flow (Shuxing Chen)Incompressible Viscous Fluid Flows with Slip Boundary Conditions and Their Numerical Simulations (Ben-yu Guo)Global Existence and Uniqueness of the Solution for the Generalized Schrödinger-KdV System (Boling Guo, Bolin Ma & Jingjun Zhang)Anomaly Cancellation and Modularity (Fei Han, Kefeng Liu & Weiping Zhang)On Interior Estimates for Mean Curvature of Convex Surfaces in R3 and Its Applications (Jiaxing Hong)Geometric Invariant Theory of the Space — A Modern Approach to Solid Geometry (Wu-Yi Hsiang)Optimal Convergence Rate of the Binomial Tree Scheme for American Options and Their Free Boundaries (Lishang Jiang & Jin Liang)Rademacher Φ Function, Jacobi Symbols, Quantum and Classical Invariants of Lens Spaces (Bang-He Li & Tian-Jun Li)Historical Review on the Roles of Mathematics in the Study of Aerodynamics (Jiachun Li)Toward Chern–Simons Theory of Complexes on Calabi–Yau Threefolds (Jun Li)Exact Boundary Synchronization for a Coupled System of Wave Equations (Tatsien Li)Scaling Limit for Compressible Viscoelastic Fluids (Xianpeng Hu & Fang-Hua Lin)Uniqueness Modulo Reduction of Bergman Meromorphic Compactifications of Canonically Embeddable Bergman Manifolds (Ngaiming Mok)The Application of Conditional Nonlinear Optimal Perturbation to Targeted Observations for Tropical Cyclone Prediction (Mu Mu, Feifan Zhou, Xiaohao Qin & Boyu Chen)Isometric Immersions in Minkowski Spaces (Yi-Bing Shen)Remarks on Volume Growth for Minimal Graphs in Higher Codimension (Yuanlong Xin)Separation of Variables for the Lax Pair of the Bogomolny Equation in 2+1 Dimensional Anti-de Sitter Space-Time (Zi-Xiang Zhou) Readership: Mathematicians and advanced graduate students in mathematics. Key Features:In memory of the highly distinguished mathematician Gu ChaohaoThe contributors are excellent experts, including 9 members of the CASProvides some important information on Differential Geometry, Partial Differential Equations, Mathematical Physics, etcKeywords:Differential Geometry;Partial Differential Equations;Mathematical Physics

In Memory of Gu Chaohao

Frontiers in Differential Geometry, Partial Differential Equations and Mathematical Physics

Yi Zhou

This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

Nonlinear Wave Equations

Tiehu Qin

Physics and Partial Differential Equations, The Complete Set?bridges physics and applied mathematics in a manner that is easily accessible to readers with an undergraduate-level background in these disciplines. Each volume is also sold individually. Readers who are more familiar with mathematics than physics will discover the connection between various physical and mechanical disciplines and their related mathematical models, which are described by partial differential equations (PDEs). The authors establish the fundamental equations for fields such as?electrodynamics;?fluid dynamics, magnetohydrodynamics, and reacting fluid dynamics;?elastic, thermoelastic, and viscoelastic mechanics;?the kinetic theory of gases;?special relativity; and?quantum mechanics. Readers who are more familiar with physics than mathematics will benefit from in-depth explanations of how PDEs work as effective mathematical tools to more clearly express and present the basic concepts of physics. The book describes the mathematical structures and features of these PDEs, including?the types and basic characteristics of the equations,?the behavior of solutions, and?some commonly used approaches to solving PDEs.?

Tatsien Li

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