4 problems

Consider persistent roll-wave forms emerging either from periodic forcing or naturally from dambreak-type initial data. Persistent-wave stability conjecture. Persistent wave forms…

Let $E(\lambda,\eta,\xi)$ be the Evans function associated with the hydraulic-wave spectral problem, and let $\varepsilon(\lambda,\eta,\xi)$ be the characteristic determinant of th…

Let $(F,H_L,H_R)$ define a discontinuous planar hydraulic shock in the whole space, with $2<F<F_{\text{2d}}$. A dispersion relation is $(\mu_L,\mu_R)$-weighted stable when its esse…

Consider a canal with a fixed fluid injection rate at one end and the associated homoclinic wave having the same fluid flux. Homoclinic height conjecture. The height of any resulti…