Fourier's well-known heat equation, introduced in 1822, describes how temperature changes in space and time when heat flows through a material. In general, this formulation works well to describe heat ...

The Annals of Applied Probability, Vol. 28, No. 3 (June 2018), pp. 1943-1976 (34 pages) The initial-boundary value problem for the heat equation is solved by using an algorithm based on a random walk ...

The study of controllability for parabolic and heat equations focuses on the capability to steer the temporal evolution of diffusion-dominated processes towards desired states. Central to this field ...

Rothe's method for parabolic initial boundary value problems, also known as the horizontal line method, consists of a time discretization by finite differences and leads to a sequence of boundary ...