We prove global existence, uniqueness and stability of entropy solutions with L2 initial data for a general family negative order dispersive equations. These weak are found to satisfy one-sided Hölder conditions whose coefficients decay in time. The latter result controls the height further provides way bound maximal lifespan classical from their data.

filter is one of the main components of embankment dams. by a simple but effective performance, filter protects the dam against erosion and soil scouring in impervious core caused by leakage (piping) and makes it safe. interaction between filter and erodible base soil is a complex phenomenon which is dependent upon several factors, and has challenged researchers for better understanding the fil...

Under the frame of the (2+1)-dimensional zero curvature equation and Tu model, the (2+1)-dimensional dispersive long wave hierarchy is obtained. Furthermore, the loop algebra is expanded into a larger one. Moreover, a class of integrable coupling system for dispersive long wave hierarchy and (2+1)-dimensional multi-component integrable system will be investigated.

We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with constant impedance exhibit no effective dispersion. We show that a new kind of effective dispersion may arise in two dimensions, even in materials with const...