| We study the pattern formation arising in some nonlinear systems. The problems come from material science and biological science. We study the instability in the corresponding mathematical models and explain the pattern formation. In particular, one mathematical model we studied is an elliptic equation and the other is a degenerate parabolic system. For the elliptic equation, we study the radial symmetric solutions and the bifurcation into nonradial ones. For the parabolic system, we study the existence of traveling wave solutions and the instability of the flat front. |
