5 papers · 1 filter
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 with conservation laws
Aric Wheeler, Kevin Zumbrun
Generalizing results of \cite{MC,S} and \cite{HSZ} for certain model reaction-diffusion and reaction-convection-diffusion equations, we derive and rigorously justify weakly nonline…
Majda and ZND models for detonation: nonlinear stability vs. formation of singularities
Paul Blochas, Aric Wheeler
For the ZND model, we show also singularity formation on the downstream side for arbitrary exponentially-growing weighted norms. For the Majda model on the other hand, we establish…
Geometric optics for Rayleigh wavetrains in d-dimensional nonlinear elasticity
Aric Wheeler, Mark Williams
A Rayleigh wave is a type of surface wave that propagates in the boundary of an elastic solid with traction (or Neumann) boundary conditions. Since the 1980s much work has been don…