Xiao-Biao Lin

Professor

 Fall 2008 Schedule

  Workshop on Dynamical Systems and Nonlinear Waves,  May 29-June 5, 2008, Zhejiang Normal University, Jinhua, China.

  Workshop on Bifurcation Methods of Limit Cycles and Related Studies,   May 20-29, Shanghai Normal University, Shanghai China.

  ICMC Summer Meeting on Differential Equations, 2008 Chapter. ,  January 28 to February 01, ICMC-USP, Sao Carlos SP, Brazil

  The Second International Conference on Recent Advance in Applied Dynamical Systems. ,  June 4 -8, 2007, Zhejian Normal University, Jinhua, China

 International Conference on Recent Developments in Differential Equations and Applications ,  July 17-21, 2006, Guangzhou University, China.

 Systemes dynamiques en dimension infinie,  4 au 8 juillet, 2005, Luminy, France

 First International Conference on Recent Advances in Bifurcation Theory and Applications of Dynamical Systems,  June 8-12, 2005, JINHUA, CHINA

 Workshop on Differential Equations and its Applications,  15-17 September 2004, Istanbul Turkey

Dynamics of Partial Differential Equations

 Traveling Waves and Shock Waves,  A special session in

Fourth International Conference on Dynamical Systems and Differential Equations

Current Research Interests

• Symbolic Dynamics and Nonlinear Semiflows
• Exponential dichotomies and homoclinic orbits in functional differential equations
• Heteroclinic orbits for reatrded functional differential equations
• Transition layers for singularly perturbed delay differential equations with monotone nonlinearities
• Shadowing lemma and singularly perturbed boundary value problems
• Using Melnikov's method to solve Silnikov's problems
• Heteroclinic bifurcation and singularly perturbed boundary value problems
• Smooth Invariant Folications in Infinite Dimensional Spaces
• Local and Global Existence of Multiple Waves Near Formal Approximations
• Generalized Rankine-Hugoniot condition and shock solutions for quasilinear hyperbolic systems
• Multiple Internal Layer Solutions Generated by Spatially Oscillatory Perturbations
• Construction and Asymptotic Stability of Structurally Stable Internal Layer Solutions
• Heteroclinic and periodic cycles in a perturbed convection model
• Stability of self-similar solutions of the Dafermos regularization of a system of conservation laws
• Generalized Snell's law for weighted minimal surface in heterogeneous media
• Multistage Evolutionary Model for Carcinogenesis Mutations
• Fast solvers for 3D Poisson Equations Involving Interfaces in a Finite or Infinite Domain
• Analytic Semigroup Generated by the Linearization of a Riemann-Dafermos Solution
• Slow Eigenvalues of Self-similar Solutions of the Dafermos Regularization of a System of Conservation Laws: an Analytic Approach
•  L2 Semigroup and Linear Stability for Riemann solutions of Hyperbolic Conservation Laws
•  Gearhart-Pruss theorem and linear stability for Riemann solutions of conservation laws
•  Algebraic dichotomies and the stability of Riemann solutions of conservation laws
•  Travelling Wave Solutions for the Painleve-Integrable Coupled KdV Equations
•  Collapsing and explosion waves in phase transitions with metastability, existence, stability and related Riemann problems