Colloquium/Seminar

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Event(s) on April 2011


  • Friday, 1st April, 2011

    Title: Global Dynamics and Traveling Fronts of Reaction-diffusion System Arising from Auto-Catalysis
    Speaker: Prof. Qi Yuanwei, Department of Mathematics, University of Central Florida, USA
    Time/Place: 11:30  -  12:30
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: In this talk, I shall report some of my recent works on global dynamics and traveling wave fronts in an isothermal chemical reaction $ A + 2B -> 3B$ involving two chemical species, a reactant $A$ and an auto-catalyst$B$ whose diffusion coefficients, $D_A$ and $D_B$, are unequal due to different molecular weights and/or sizes. We give detailed analysis of large time behaviour when initial values decay to zero at infinity. In addition, Explicit bounds $v_*$ and $v^*$ that depend on $D_B/D_A$ are derived such that there is a unique travelling wave of every speed $v >= v^*$ and there does not exist any travelling wave of speed $v < v_*$.


  • Tuesday, 12th April, 2011

    Title: Upper and Lower Solutions for Stochastic Differential Equations under G-Brownian Motion
    Speaker: Prof. Piao Daxiong, Department of Mathematics, School of Mathematical Sciences, Ocean University of China, China
    Time/Place: 10:00  -  11:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The method of upper and lower solutions for vector valued stochastic differential equations under G-Brownian motion is developed. The existence of solutions for the stochastic differential equations under G-Brownian motion having discontinuous drift coefficients is established with the method of upper and lower solutions. As an example the unit step function with a scalar stochastic differential equation under G-Brownian motion is considered.


  • Tuesday, 12th April, 2011

    Title: Numerical Renormalization Group Methods for finite-time singular self-similar solutions
    Speaker: Dr. Huang Yanghong, Department of Mathematics, Simon Fraser University, Canada
    Time/Place: 11:00  -  12:00
    FSC1217, Fong Shu Chuen Library, HSH Campus, Hong Kong Baptist University
    Abstract: The long time or finite time singular solutions of nonlinear partial differential equations with generic initial data are usually self similar, either of the relatively simple first kind or of the second kind (with anomalous exponents). These self similar profiles can be obtained by post-processing the simulation data, though not efficient because of the long simulation time or the singularity in the solution. In this talk, we present a numerical renormalization group (RG) method to calculate these second kind self-similar profiles. Instead of finding the singular solutions, this RG procedure converges to the stable self-similar profiles as a fixed point iteration. We also demonstrate the effectiveness of this method by several numerical experiments.

 

 


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