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 ...

Any straight line graph has a constant gradient, which is calculated by the change in 𝑦 divided by the change in 𝑥, along any section of the graph. The gradient is measuring the steepness of the ...

SIAM Journal on Numerical Analysis, Vol. 49, No. 5/6 (2011), pp. 2017-2038 (22 pages) General autonomous stochastic differential equations (SDEs) driven by one-dimensional Brownian motion in the ...

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 ...