This paper presents a general result on the existence of global smooth solutions to
hyperbolic systems of balance laws in several space variables. We propose an entropy …

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

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 …

Following the pointwise semigroup approach of [ZH, MZ. 1], we establish sharp pointwise
Green function bounds and consequent linearized stability for viscous shock profiles of …

This paper presents an observation that under reasonable conditions, many partial
differential equations from mathematical physics possess three structural properties. One of …

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 …

Extending the work of Yang–Zumbrun for the hydrodynamically stable case of Froude
number F< 2, we categorize completely the existence and convective stability of hydraulic …

We consider reaction-diffusion equations that are stochastically forced by a small
multiplicative noise term. We show that spectrally stable traveling wave solutions to the …

Combining pointwise Green's function bounds obtained in a companion paper [36] with
earlier, spectral stability results obtained in [16], we establish nonlinear orbital stability of …

We consider nonlinear hyperbolic systems with a general source and prove that for
appropriately chosen smooth initial data the lifespan of the associated C 1-solution u cannot …