Tianyuan Mathematical Center
in Southwest China

Pattern formation in nonlocal diffusion equations

报告专家：Peter Bates（Michigan State University）

报告时间：7月17日 14:00-15:00

报告地点：数学学院西303报告厅

报告摘要：

Many physical and biological processes occur with long-range interaction, giving rise  to equations with nonlocal-in-space operators in place of the usual Laplacian. These  operators are diffusive-like but are bounded rather than unbounded as is the case of  the local diffusion operator.  

With the Laplacian representing diffusion, Alan Turing, in 1952, showed that stable  patterned states may form from small perturbations of homogeneous stationary states for certain systems of reaction-diffusion equations. By establishing a spectral convergence result, it is shown that similar pattern  formation occurs when the Laplacian is replaced by nonlocal diffusion operators,  when scaled appropriately.  

Some questions concerning global bifurcation will also be mentioned.