8 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 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…
Continuous guts poker and numerical optimization of generalized recursive games
Kevin Buck, Jae Hwan Lee, Jacob Platnick +2
We study a type of generalized recursive game introduced by Castronova, Chen, and Zumbrun featuring increasing stakes, with an emphasis on continuous guts poker and v. coal…
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…
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…
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…