Recent progress on reaction-diffusion systems and viscosity solutions /

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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor Corporativo: International Conference on Reaction-Diffusion Systems and Viscosity Solutions
Otros Autores: Du, Yihong, Ishii, Hitoshi, 1947-, Lin, Wei-Yueh
Formato: Electrónico Congresos, conferencias eBook
Idioma:Inglés
Publicado: Hackensack, NJ : World Scientific, ©2009.
Temas:
Reaction-diffusion equations > Congresses.
Differential equations, Parabolic > Congresses.
Équations de réaction-diffusion > Congrès.
Équations différentielles paraboliques > Congrès.
MATHEMATICS > Differential Equations > General.
Differential equations, Parabolic
Reaction-diffusion equations
Mathematics.
Physical Sciences & Mathematics.
Calculus.
Conference papers and proceedings
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • 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
  • 2.2. 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
  • T.

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