Nonlinear stability in seismic waves

Nonlinear Stability of Semidiscrete Shock Waves

The orbital stability of possibly large semi-discrete shock waves is considered. These waves are traveling wave solutions of discrete in space and continuous in time systems of conservation laws, which constitute a class of Lattice Dynamical Systems. The underlying lattice xZis by nature not invariant by change of frame. Thus semi-discrete shock waves cannot really be transformed into stationar...

Stability of nonlinear waves: pointwise estimates

This is an expository article containing a brief overview of key issues related to the stability of nonlinear waves, an introduction to a particular technique in stability analysis known as pointwise estimates, and two applications of this technique: time-periodic shocks in viscous conservation laws [BSZ10] and source defects in reaction diffusion equations [BNSZ12, BNSZ14].

Nonlinear Stability of Viscous Roll Waves

Extending results of Oh–Zumbrun and Johnson–Zumbrun for parabolic conservation laws, we show that spectral stability implies nonlinear stability for spatially periodic viscous roll wave solutions of the one-dimensional St. Venant equations for shallow water flow down an inclined ramp. The main new issues to be overcome are incomplete parabolicity and the nonconservative form of the equations, w...

Nonlinear Stability of Viscous Shock Waves

On Nonlinear Water Waves in a Channel