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.
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