Author Hua, Zhen
Title Differential Equations and Asymptotic Theory in Mathematical Physics : Wuhan University, Hubei, China, 20-29 October 2003
Imprint Singapore : World Scientific Publishing Co Pte Ltd, 2004
©2004
book jacket
Descript 1 online resource (389 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Series in Analysis Ser. ; v.2
Series in Analysis Ser
Note Intro -- CONTENTS -- Preface -- PART I MINI-COURSES -- Ismail, Mourad E. H. Lectures on Orthogonal Polynomials -- 1. Construction of Orthogonal Polynomials -- 2. Some Properties of Orthogonal Polynomials -- 3. Differential Equations -- 4. Electrostatic Equilibrium Problems -- 5. Generating Functions and Asymptotics -- 6. Applications -- 7. Zeros of Orthogonal Polynomials and Eigenvalues -- Acknowledgments. -- References -- Ramis, Jean-Pierre Gevrey Asymptotics and Applications to Holomorphic Ordinary Differential Equations -- 0. Introduction -- 1. Asymptotic expansions -- 1.1. Classical asymptotics (or Poincare' asymptotics) -- 1.2. Gevrey asyrnptotics -- 1.3. k-summability -- 1.4. Laplace transform -- 1.5. Ramis-Sibuya theorem and k-summability -- 2. Applications to ordinary differential equations -- 2.1. Linear ordinary differential equations, index theorem and Newton polygons -- 2.2. Fundamental existence theorems -- 3. Multisummability -- 4. Gevrey asymptotic and singular perturbations -- 4.1. Delay in bifurcations -- References -- Ward, Michael J. Spikes for Singularly Perturbed Reaction-Diffusion Systems and Carrier's Problem -- 1. Introduction -- 2. Spike Equilibria for Scalar Problems -- 2.1. Interior Spike Solutions: No Boundary Layers -- 2.2. Interior Spike Solutions: Boundary Layers -- 2.3. Exponential Sensitivity to the Data -- 2.4. Related Problems: One Space Dimension -- 2.5. Spikes for Quasilinear Elliptic PDE -- 3. Spikes for Nonlocal Scalar Problems -- 3.1. The Shadow Gierer-Meinhardt Model -- 3.2. Hopf Bifurcations for the Shadow GM Model -- 3.3. A Microwave Heating Model -- 3.4. A Flame-Front Evolution Model -- 4. Dynamics and Equilibria of a Spike in an R-D System -- 4.1. The Near-Shadow System -- 4.2. Pinning of a Spike -- 4.3. Sudden Oscillatory Instabilities -- 5 . Multi-Spike Solutions in Reaction-Diffusion Systems
5.1. Gray-Scott Model (Low Feed-Rate): Equilibrium -- 5.2. Gray-Scott Model (High Feed-Rate): Equilibrium -- 5.3. Stability of Multi-Spike Equilibria: One Dimension -- 6. Concluding Remarks -- Acknowledgments -- References -- Wong, Roderick S. C. Five Lectures on Asymptotic Theory -- LECTURE I STATIONARY PHASE APPROXIMATION -- 1. Introduction -- 2. Stationary-Phase Approximation -- 3. Coalescing Stationary Points -- 4. Two-dimensional Approximation -- 5. A Uniform Asymptotic Formula -- References -- LECTURE II METHOD OF STEEPEST DESCENT -- 1. Introduction -- 2. The Airy Integral -- 3. Stokes' Phenomenon -- 4. Adjacent Saddle and Adjacent Contour -- 5. Exponential Asymptotics -- 6. Hyperasymptotics -- References -- LECTURE III WKB METHOD AND TURNING POINT -- 1. Introduction -- 2. Successive Approximations -- 3. Turning Point Problem -- 4. Simple Pole -- 5. Examples -- References -- LECTURE IV BOUNDARY LAYER THEORY -- 1. Introduction -- 2. Derivation of (1.3) -- 3. Internal Layers -- 4. Carrier-Pearson Equation -- References -- LECTURE V DIFFERENCE EQUATIONS AND ORTHOGONAL POLYNOMIALS -- 1. Introduction -- 2. Normal and Subnormal Series -- 3. Equation (1.2) with p and q 0. -- 4. Airy-type Expansion -- 5. Bessel-type Expansion -- References -- PART II INVITED PAPERS -- Bohun, C. S., Frigaard, I., Huang, H.X. and Liang S. Q. A Perturbation Model for the Growth of Type III-V Compound Crystals -- 1. Introduction -- 2. Mathematical Model and Dimensional Analysis -- 2.1. Non- dimensionalization -- 3. Perturbation Solution -- 3.1. Resolution of the zeroth order model -- 3.1.1. Constant radius crystals -- 3.1.2. Conical crystals -- 3.1.3. Comments -- 3.2. Radial variations: resolution of the first order model -- 3.2.1. Constant radius crystals -- 3.2.2. Conical crystals -- 4. Thermal Stress -- 4.1. Plain strain assumption -- 4.2. Results -- 5. Conclusion
Acknowledgement. -- References -- Chen, H. and Yu, C. Asymptotic Behaviour of the Trace for Schrodinger Operator on Irregular Domains -- 1. Main Result -- 2. Preparation -- 3. Proof of the Main Results -- 4. Further Results -- References -- Jiang, L. S. and Ren, X. M. Limitations and Modifications of Black-Scholes Model -- 1. Introduction -- 1.1. Motivation of Black-Scholes model -- 1.2. Foundations of Black-Scholes model -- 1.3. Modifications of the model -- 2. Jump-diffusion process -- 2.1. Movement of asset price -- 2.2. Black-Scholes model with jump-diffusion -- 2.3. Some results -- 3. Stochastic interest rate -- 3.1. The models of stochastic interest rate -- 3.2 Black-Scholes model with stochastic interest rate -- 3.2. American style option-valuation of mortgage -- 4. Variable volatility & implied volatility -- 4.1. Implied volatility surface -- 4.2. Related Optimal Control Problem -- 4.3. Numerical results -- References -- Li, T.T. (Li, Daqian) Exact Boundary Controllability of Unsteady Flows in a Network of Open Canals -- 1. Introduction -- 2. General consideration -- 3. Statement on the exact boundary controllability of unsteady flows in a network of open canals -- 4. Preliminaries for quasilinear hyperbolic systems of diagonal form -- 5. Corresponding consideration for Saint-Venant system -- 6. Exact boundary controllability of unsteady flows in a tree-like network of open canals -- 7. Some remarks -- References -- Miyake, M. and Ichinobe, K. Hierarchy of Partial Differential Equations and Fundamental Solutions Associated with Summable Formal Solutions of a Partial Differential Equation of non Kowalevski Type -- 1. Introduction -- 2. (0)-Gevrey summability (Review) -- 3. The case of entire function Cauchy data -- 4. Proof of Proposition 1 -- 5. Hierarchy of differential equations and fundamental solutions -- 6. Singular perturbation
References -- Tahara, H. On the Singularities of Solutions of Nonlinear Partial Differential Equations in the Complex Domain, II -- 1. Introduction -- 2. Non-existence of singularities -- 3. Criteria for the existence of singularities -- 4. Sufficient conditions for the existence of singularities -- References -- Tan, Y . J. and Chen, X. X. Identifying Corrosion Boundary by Perturbation Method -- 1. Introduction -- 2. Perturbation Solution for Direct Problem -- 3. Reconstruct Free Boundary -- 4. Numerical Examples -- 5. Some Theoretical Results -- References -- Wei, J. C. Existence and Stability of Lamellar and Wriggled Lamellar Solutions in the Diblock Copolymer Problem -- 1. Introduction -- 2. One-dimensional Local Minimizers -- 3. Stability of the Perfect Lamellar Solutions in 2D -- 4. Existence of Wriggled Lamellar Solutions -- 5. Stability of the Bifurcating Solutions -- Acknowledgments. -- References
This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves. The proceedings have been selected for coverage in:. • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings). • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). • CC Proceedings — Engineering & Physical Sciences
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Hua, Zhen Differential Equations and Asymptotic Theory in Mathematical Physics : Wuhan University, Hubei, China, 20-29 October 2003 Singapore : World Scientific Publishing Co Pte Ltd,c2004 9789812560551
Subject Differential equations.;Mathematical physics -- Asymptotic theory
Electronic books
Alt Author Wong, R