The study of Lagrangian equations and gradient estimates occupies a critical niche at the intersection of partial differential equations, differential geometry, and variational calculus. Lagrangian ...

All straight line graphs have an equation that can be written in the form 𝑦 equals 𝑚𝑥 add 𝑐, where 𝑚, the coefficient of the 𝑥 term, is the gradient or slope of the line. The constant, 𝑐, is ...

We present a Godunov-type scheme for the shallow water equations with horizontal temperature gradient and variable topography. First, the exact solutions of the Riemann problem in a computational form ...