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035    (MiAaPQ)EBC296108 
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040    MiAaPQ|beng|erda|epn|cMiAaPQ|dMiAaPQ 
050  4 QA370.D493 2004 
082 0  515 
100 1  Hua, Zhen 
245 10 Differential Equations and Asymptotic Theory in 
       Mathematical Physics :|bWuhan University, Hubei, China, 20
       -29 October 2003 
264  1 Singapore :|bWorld Scientific Publishing Co Pte Ltd,|c2004
264  4 |c©2004 
300    1 online resource (389 pages) 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
490 1  Series in Analysis Ser. ;|vv.2 
505 0  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 
505 8  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 
505 8  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 
505 8  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 
520    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 
588    Description based on publisher supplied metadata and other
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590    Electronic reproduction. Ann Arbor, Michigan : ProQuest 
       Ebook Central, 2020. Available via World Wide Web. Access 
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650  0 Differential equations.;Mathematical physics -- Asymptotic
       theory 
655  4 Electronic books 
700 1  Wong, R 
776 08 |iPrint version:|aHua, Zhen|tDifferential Equations and 
       Asymptotic Theory in Mathematical Physics : Wuhan 
       University, Hubei, China, 20-29 October 2003|dSingapore : 
       World Scientific Publishing Co Pte Ltd,c2004
       |z9789812560551 
830  0 Series in Analysis Ser 
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