September 1, 2019 at 9:00 pm

Mathematical Biology Seminar | Nonlinear Stability at the Zigzag Boundary, Sept. 17

Qiliang Wu, portrait in office

Dr. Qiliang Wu

The Dynamical Systems and Mathematical Biology Seminar features Dr. Qiliang Wu discussing “Nonlinear Stability at the Zigzag Boundary” on Tuesday, Sept. 17, from 3:05 to 4 p.m. in Morton 318.

Wu is Assistant Professor of Mathematics at Ohio University.

Abstract: We investigate the dynamics of roll solutions at the zigzag boundary of the planar Swift-Hohenberg equation. Linear analysis shows an algebraic decay of small perturbation with a $t^{-1/4}$ rate, instead of the classical $t^{-1/2}$ diffusive decay rate, due to the degeneracy of the quadratic term of the continuation of the translational mode of the linearized operator in the Bloch-Fourier spaces. The proof is based on a decomposition of the neutral mode and the faster decaying modes in the Bloch-Fourier space, and a fixed-point argument, demonstrating the irrelevancy of the nonlinear terms.

Leave a Reply

Your email address will not be published. Required fields are marked *