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 ...

The Gorlin equation is used to calculate mitral or aortic valve area during invasive hemodynamic assessment via cardiac catheterization. While initially developed to measure mitral valve area in ...

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 ...