4 papers
Nonlinear stability of two-dimensional periodic waves in parabolic systems with conservation laws
L. Miguel Rodrigues, Aric Wheeler
We develop a stability theory for two-dimensional periodic traveling waves of general parabolic systems, possibly including conservation laws. In particular, we identify a diffusiv…
Linear stability analysis for a system of singular amplitude equations arising in biomorphology
Aric Wheeler, Kevin Zumbrun
We study linear stability of exponential periodic solutions of a system of singular amplitude equations associated with convective Turing bifurcation in the presence of conservatio…
Convective Turing Bifurcation
Aric Wheeler, Kevin Zumbrun
Following the approach pioneered by Eckhaus, Mielke, Schneider, and others for reaction diffusion systems [E, M1, M2, S1, S2, SZJV], we systematically derive formally by multiscale…
Diffusive stability of convective Turing patterns
Aric Wheeler, Kevin Zumbrun
Following the approach of [E1, M1, M2, S1, S2, SZJV] for reaction diffusion systems, we justify rigorously the Eckhaus stability criterion for stability of convective Turing patter…