We present a new method of investigating the so-called quasi-linear strongly damped wave equations ∂ t u− γ∂t∆xu−∆xu+ f(u) = ∇x · φ ′(∇xu) + g in bounded 3D domains. This method allows us to establish the existence and uniqueness of energy solutions in the case where the growth exponent of the non-linearity φ is less than 6 and f may have arbitrary polynomial growth rate. Moreover, the existenc...

We consider traveling wave solutions to a class of diierential-diierence equations. Our interest is in understanding propagation failure, directional dependence due to the discrete Laplacian, and the relationship between traveling wave solutions of the spatially continuous and spatially discrete limits of this equation. The diierential-diierence equations that we study include damped and undamp...

For a linear transport equation in one space dimension with speeds in a compact interval and a general symmetric kernel for the change of velocity a problem with free boundary (Stefan problem) is stated. The case of constant speed corresponds to a Stefan problem for the damped wave equation (telegraphers equation). Existence and uniqueness of the free boundary is shown, and the connection to th...

For the SEG-EAGE salt data set, common-azimuth migration produces better images in the subsalt than single-arrival Kirchhoff migration, at a similar computational cost. Subsalt reflectors are better imaged and the typical Kirchhoff artifacts caused by severe multipathing disappear. We show how angle-domain Common Image Gathers (CIG) can be easily extracted from prestack wavefield downward conti...