Pattern formation in nonlocal diffusion equations
报告专家：Peter Bates（Michigan State University）
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.