论文标题
锯齿形边界的非线性稳定性
Nonlinear Stability at the Zigzag Boundary
论文作者
论文摘要
我们研究了平面Swift-Hohenberg方程的曲折边界的滚动溶液的动力学。线性分析表明，由于$ t^{ - 1/4} $速率的小扰动代数衰减，而不是经典的$ t^{ - 1/2} $扩散的衰减率，这是由于Bloch-Fourier Space中线性操作员的翻译模式的延续的持续延续的延续性术语的脱落。该证明是基于中性模式的分解和Bloch较大空间中更快的衰减模式的分解，以及一个定点参数，证明了非线性项的无关紧要。
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.
