Oblique and Checkerboard Patterns in the Quenched Cahn–Hilliard Model

We consider transversely modulated fronts in a directionally quenched Cahn–Hilliard equation, posed on two-dimensional infinite channel, with both parameter and source-term type heterogeneities. Such quenching heterogeneities travel through the domain, excite instabilities, can select pattern formed their wake. particular study striped patterns which are oblique to direction as well checkerboard patterns. Under generic spectral assumptions, these arise via an O(2)-Hopf bifurcation speed is varied, symmetries arising from translations reflections transverse variable. employ abstract functional analytic approach establish such near point. Exponential weights used address neutral continuous spectrum, co-domain restriction mass-flux. also give method determine of fronts. then explicit example for our hypotheses satisfied bifurcating be investigated numerically.