1 citations · 1 across the 2 of their papers we have counts for
7 papers
Existence and behavior of steady solutions on an interval for general hyperbolic-parabolic systems of conservation laws
Benjamin Melinand, Kevin Zumbrun
We study the inflow-outflow boundary value problem on an interval, the analog of the 1D shock tube problem for gas dynamics, for general systems of hyperbolic-parabolic conservatio…
Pseudodifferential damping estimates and stability of relaxation shocks
Kevin Zumbrun
A bottleneck in the theory of large-amplitude and multi-d viscous and relaxation shock stability is the development of nonlinear damping estimates controlling higher by lower deriv…
Linear damping estimates for periodic roll wave solutions of the inviscid Saint-Venant equations and related systems of hyperbolic balance laws
L. Miguel Rodrigues, Kevin Zumbrun
Substantially extending previous results of the authors for smooth solutions in the viscous case, we develop linear damping estimates for periodic roll-wave solutions of the invisc…
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…