Heat equation as a Friedrichs system

Friedrichs Extension Theorem

Some notes on the Friedrichs Extension Theorem, for MATH 7130, Spring 2010.

Geometric Heat Equation and

We propose a geometric smoothing method based on local curvature in shapes and images which is governed by the geometric heat equation and is a special case of the reaction-diiusion framework proposed by 28]. For shapes, the approach is analogous to the classical heat equation smoothing, but with a renormalization by arc-length at each innnitesimal step. For images, the smoothing is similar to ...

Heat Equation and Potential Burgers Equation

In this work, we construct the general solution to the Heat Equation (HE) and to many tensor structures associated to the Heat Equation, such as Symmetries, Lagrangians, Poisson Brackets (PB) and Lagrange Brackets (LB), using newly devised techniques that may be applied to any linear equation (e.g., Schrödinger Equation in field theory, or the small-oscillations problem in mechanics). In partic...

The Heat Equation

A Probability Approach to the Heat Equation

0. Introduction. Let u be a function whose domain is some open set in a Euclidean space. Then, under various conditions on u, there is a well defined first boundary value (Dirichlet) problem, involving an analysis of the boundary points of the domain, and a more or less closely associated problem of the existence of boundary limits of u. The evaluation of u in terms of the boundary function thu...