國家理論科學研究中心
 NCTS An Intensive Course in
 Reaction-Diffusion Systems with Application to Spatial Ecology

 


Speaker: Professor Yihong Du  杜一宏
 
             (University of New England, Australia)


Time : Every Thursday 10:00am-12:00pm in March 22 ~ April 19
 

Abstracts:
We discuss the classical and degenerate logistic model and several two
species competition and predator-prey models, where spatial heterogeneity plays a fundamental role. In particular, the results will be carefully compared with thecorresponding homogeneous cases of the same model, toreveal the effects of spatial heterogeneity on the models. The course gives a systematic presentation of several recent works of the lecturer and collaborators.

  Outline:
  1. The classical and degenerate diffusive logistic model
  2. The classical diffusive competition and predator-prey models
  3. The degenerate competition model and its perturbation
  4. The degenerate predator-prey models and perturbation
  5. A predator-prey model with a protection zone
  6. The competition model with a protection zone
 

References:
(a) Book and survey papers:
1. Y. Du, Order Structure and Topological Methods in Nonlinear Partial
Differential Equations, Vol. 1, World Scientific, 2006. (Chatper 5, see also the appendix for background material in PDE)
2. Y. Du and J. Shi, Some recent results on diffusive predator-prey models in spatially heterogeneous environment, in Nonlinear Dynamics and Evolution Equations, Eds. Hermann Brunner, Xiao-Qiang Zhao and Xingfu Zou, Fields Institute Communications Vol. 48, American Math. Soc., 2006, pp. 95-135.
3. Y. Du,  Bifurcation and related topics in elliptic problems, Handbook for
Partial Diff. Eqns.-Stationary Partial Differential Equations, Vol.
2, Eds. M. Chipot and P. Quittner, Elsevier, 2005, pp.127-209. (Section 3)
4. Y. Du, Spatial patterns for population models in a heterogeneous
environment,  Taiwanese J. Math., 8(2004), 155-182.

(b) Research papers:
1. Y. Du and Xing Liang, A diffusive competition model with a protection
zone, preprint.
2. Y. Du and Junping Shi, A diffusive predator-prey model with a protection zone, J. Diff. Eqns., 229(2006), 63-91.
3. Y. Du and Z-M. Guo, The degenerate logistic model and a singularly mixed boundary blow-up problem, Discrete and Continuous Dynamical  Systems, 14(2006), 1-29.
4. Y. Du and S.B. Hsu, A diffusive predator-prey model in heterogeneous
environment, J. Diff. Eqns., 203(2004), 331-364.
5. Y. Du, Realization of prescribed patterns in the competition model, J. Diff. Eqns., 193(2003), 147-179.
6. Y. Du and Shujie Li, Positive solutions with prescribed patterns in
some simple semilinear equations, Diff. Integral Eqns. 15(2002), 805-822.
7. Y. Du, Effects of a degeneracy in the competition model, part I and II, J. Diff. Eqns., 181(2002), 92-164.
8. E.N. Dancer and Y. Du, Effects of certain degeneracies in the predator-prey model, SIAM J Math. Anal., 34(2002), 292-314.
9. Y. Du and Q. Huang, Blow-up solutions for a class of semilinear elliptic and parabolic equations, SIAM J. Math. Anal., 31(1999), 1-18.

 Place      

Lecture Room A

National Center for Theoretical Sciences
4th Floor, the 3rd General Building,

National Tsing Hua University