Considered as rest points of ODE on Lp, stationary viscous shock waves present a critical
case for which standard semigroup methods do not suffice to determine stability. More …

We summarize recent progress on one-dimensional and multidimensional stability of
viscous shock wave solutions of compressible Navier–Stokes equations and related …

Physical and mathematical considerations warrant the inclusion of regularizing effects such
as diffusion, dissipation, and/or relaxation in the study of stability of shock waves, particularly …

We establish nonlinear L 1∩ H 3→ L p orbital stability, 2≦ p≤∞, with sharp rates of decay,
of large-amplitude Lax-type shock profiles for a class of symmetric hyperbolic-parabolic …

We prove a posteriori error estimates for a finite element method for systems of strictly
hyperbolic conservation laws in one space dimension, and design corresponding adaptive …

We establish sharp pointwise Green's function bounds and consequent linearized stability
for smooth traveling front solutions, or relaxation shocks, of general hyperbolic relaxation …

We establish one-dimensional spectral stability of small amplitude viscous and relaxation
shock profiles using Evans function techniques to perform a series of reductions and normal …

We consider a hyperbolic–parabolic system arising from a chemotaxis model in tumor
angiogenesis, which is described by a Keller–Segel equation with singular sensitivity. It is …

We consider the L 2-contraction up to a shift for viscous shocks of scalar viscous
conservation laws with strictly convex fluxes in one space dimension. In the case of a flux …

We study the time-asymptotic behavior of weak rarefaction waves of systems of conservation
laws describing one-dimensional viscous media, with strictly hyperbolic flux functions. Our …