Record:   Prev Next
Author Du, Yihong
Title Recent Progress On Reaction-diffusion Systems And Viscosity Solutions
Imprint Singapore : World Scientific Publishing Company, 2009
©2009
book jacket
Descript 1 online resource (373 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Note CONTENTS -- Preface -- Long-Time Dynamics in Semilinear Parabolic Problems with Autocatalysis N. Ackermann -- 1. Introduction -- 2. Generalities -- 2.1. Existence of the Parabolic Flow -- 2.2. Invariant Sets -- 2.3. Invariant Order Relations -- 2.4. Blow- Up in Finite Time and A Priori Bounds -- 3. Existence of Equilibria and Connecting Orbits -- 3.1. Invariant Manifolds and the Comparison Principle -- 3.2. The Definite Homogeneous Case -- 3.3. Invariant Manifolds and the Zero Number -- 3.4. Invariant Manifolds and Linking Theorems -- 3.5. Order Intervals, Sub- and Supersolutions -- Acknowledgment -- Bibliography -- A Note on Reaction-Diffusion Systems with Skew-Gradient Structure C.-N. Chen, T.-L. Horng, D. Lee and G.-H. Tsai -- 1. Introduction -- 2. Stability Criteria -- 3. Applications of Theorem 1 and Theorem 2 -- 4. Numerical Results -- 4.1. -- 4.2. -- Acknowledgments -- References -- Change of Environment in Model Ecosystems: Effect of a Protection Zone in Diffusive Population Models Y. Du -- 1. Introduction -- 2. The competition model -- 2.1. Preliminaries -- 2.2. Main results -- 3. The Holling type II predator-prey model -- 3.1. Protection zone above critical size -- 3.2. Protection zone below critical size -- 4. The Leslie predator-prey model -- References -- The State of the Art for a Conjecture of de Giorgi and Related Problems A. Farina and E. Valdinoci -- 1. De Giorgi conjecture -- 1.1. (Crude) physical motivation -- 1.2. Possible motivation for the conjecture -- 2. Available results -- 2.1. The case n = 2 -- 2.1.1. First proof of Conjecture 1.1 for n = 2 -- 2.1.2. Second proof of Conjecture 1.1 for n = 2 -- 2.2. The case n = 3 -- 2.3. The case 4 n 8 -- 2.4. The case of the quasiminima -- 2.5. The case in which the level sets are global graphs -- 2.6. The fully nonlinear case -- 2.7. The fractional Laplacian case
2.8. The Heisenberg group case -- Acknowledgments -- References -- Two Remarks on Periodic Solutions of Hamilton-Jacobi Equations H. Ishii and H. Mitake -- 1. Introduction -- 2. Existence of periodic solutions -- 3. Constancy on Aubry sets -- Acknowledgments -- References -- Asymptotic Expansion Method for Local Volatility Models N. Ishimura and K. Nishida -- 1. Introduction -- 2. Proof of Theorem -- 3. Discussions -- Acknowledgments -- References -- Recent Developments on Maximum Principle for LP-Viscosity Solutions of Fully Nonlinear Elliptic/Parabolic PDEs s. Koike -- 1. Introduction -- 2. Preliminaries -- 3. Elliptic PDEs -- 3.1. Linear growth (i.e. (1) and (2)) -- 3.2. Superlinear growth (i.e. (3) and (4)) -- 3.3. Linear and superlinear growth -- 4. Parabolic PDEs -- 4.1. Bounded coefficients (i.e. (1)) -- 4.2. Linear growth (i.e. (2) and (3)) -- 4.3. Superlinear growth (i.e. (4) and (5)) -- 4.4. Linear and superlinear growth -- References -- Multiscale Modeling of Electrical Activities of the Heart C.-P. Lo, H.-C. Tien, D. Lee and C.-H. Chang -- 1. Introduction -- 2. Cellular or subcellular level modeling (microscopic): Ordinary differential equations -- 3. Tissue level modeling (mesoscopic) -- 4. Whole heart modeling (macroscopic) -- 4.1. Buildup of geometric model of heart -- 4.2. Numerical methods -- 4.3. EGG computing -- 5. Applications in hear arrhythmia -- 6. Conclusion -- References -- Symmetry Properties of Positive Solutions of Parabolic Equations: A Survey P. Polacik -- 1. Introduction: basic problems, results and some history -- 1.1. Equations on bounded domains -- 1.2. Equations on ]RN -- 1.3. Cooperative systems -- 1.4. Applications -- 2. General notation -- 3. Fully nonlinear equations on bounded domains -- 3.1. Solutions on (0,00) -- 3.2. Solutions: (-00, T) and linearized problems -- 3.3. Asymptotically symmetric equations
4. Quasilinear equations on ]RN -- 4.1. Solutions on (0, ) -- 4.2. Solutions on (- , T) and linearized problems -- 5. Cooperative systems -- 6. On the proofs: a comparison of bounded and unbounded domains -- 7. Applications and some open problems -- References -- Travelling Pulse Waves Non-Vanishing at Infinity for the Derivative Nonlinear Schrodinger Equation K. Imamura and K. Sakamoto -- 1. Introduction and main result -- 2. Existence of travelling pulse waves -- 2.1. Homoclinic orbits -- 2.2. Small and Large pulse waves ¢S,L -- 3. Spectral property of pulse wave solutions -- References -- Threshold and Redistancing Dynamics for Geometric Motions S. Esedoglu, S. J. Ruuth and R. Tsai -- 1. Introduction -- 2. Expansions, Truncations, and Thresholding -- 2.1. Expansions Near the Curve -- 2.2. Trancations and Thresholding -- 2.2.1. Willmore with Lower Order Terms -- 2.2.2. Surface Diffusion -- 2.3. Signed Distance Function to a Smooth Curve and Redistancing -- 2.3.1. General Curvature Motions -- 3. Numerical Implementations and Experiments -- 3.1. Expanding Circle -- 3.2. Combined Curvature and Willmore Motion -- 3.3. Surface Diffusion Flow -- 3.4. Shape Reconstruction -- 3.5. Junctions -- 3.6. General Curvature Motion Using Signed Distance Functions and Redistancing -- 4. Conclusions -- References -- Blow-Up Problems for Partial Differential Equations and Systems of Parabolic Type y. Chen and M. Wang -- 1. Introduction -- 2. Simultaneous blow-up -- 3. Systems with homogeneous Dirichlet boundary conditions -- 4. Nonlinear Boundary Value Problem -- 5. Initial and boundary value problems with localized terms -- 6. Degenerate problems not in divergence form -- 7. Non-local problems -- Acknowledgment: -- References -- Global Solutions for the Shigesada-Kawasaki-Teramoto Model with Cross-Diffusion Y. Yamada -- 1. Problems -- 2. Global existence results
3. A priori estimate -- 4. Proofs of theorems -- 1. Idea of proof of Theorem 2.3 -- II. Outline of proofs of Theorems 2.4 and 2.5 -- III. Idea of proof of Theorem 2.6 -- IV. Idea of proof of Theorem 2.7 -- 5. Concluding remarks -- References -- Dynamics of Global Solutions of a Semilinear Parabolic Equation E. Yanagida -- 1. Introduction -- 2. Properties of steady states -- 2.1. Critical exponents -- 2.2. Asymptotic behavior of steady states -- 3. Attractivity properties of steady states -- 3.1. Stability of steady states -- 3.2. Approach of two solutions -- 3.3. Rate of approach -- 3.4. Anisotropically decaying solutions -- 4. Non-convergence and quasi-convergence -- 4.1. Non-stabilizing solutions -- 4.2. Quasi-convergence -- 4.3. Birth-and-death of peaks -- 5. Grow-up of solutions -- 5.1. A sufficient condition for grow-up -- 5.2. Grow-up rate -- 5.3. Grow-up in the critical case -- 6. Convergence to the trivial steady state -- 6.1. Sufficient conditions for the converyence to zero -- 6.2. lJecay rate -- 6.3. Slowly decaying solutions -- 7. Convergence to self-similar solutions -- 7.1. Forward self-similar solutions -- 7.2. Convergence rote -- 8. Rapidly decaying solutions -- 8.1. Linear behavior of solutions -- 8.2. Convergence to self-similar solutions of the linear heat equation -- Acknowledgments -- References -- Spatial Dynamics of Some Evolution Systems in Biology X-Q. Zhao -- 1. Introduction -- 2. Monotone systems -- 2.1. Monostable case -- 2.2. Bistable case -- 3. A class of non-monotone systems -- 4. Applications to biological systems -- 4.1. A model with a quiescent stage -- 4.2. A nonlocallattice differential system -- 4.3. A multi-type SIS epidemic model -- 4.4. A vector disease model with spatial spread -- 4.5. A nonlocal and periodic model with dispersal -- References
This book consists of survey and research articles expanding on the theme of the "International Conference on Reaction-Diffusion Systems and Viscosity Solutions", held at Providence University, Taiwan, during January 3-6, 2007. It is a carefully selected collection of articles representing the recent progress of some important areas of nonlinear partial differential equations. The book is aimed for researchers and postgraduate students who want to learn about or follow some of the current research topics in nonlinear partial differential equations. The contributors consist of international experts and some participants of the conference, including Nils Ackermann (Mexico), Chao-Nien Chen (Taiwan), Yihong Du (Australia), Alberto Farina (France), Hitoshi Ishii (Japan), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin Lo (Taiwan), Peter Polacik (USA), Kunimochi Sakamoto (Japan), Richard Tsai (USA), Mingxin Wang (China), Yoshio Yamada (Japan), Eiji Yanagida (Japan), and Xiao-Qiang Zhao (Canada)
Description based on publisher supplied metadata and other sources
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: Du, Yihong Recent Progress On Reaction-diffusion Systems And Viscosity Solutions Singapore : World Scientific Publishing Company,c2009 9789812834737
Subject Reaction-diffusion equations -- Congresses.;Differential equations, Parabolic -- Congresses
Electronic books
Alt Author Ishii, Hitoshi
Lin, Wei-yueh
Record:   Prev Next