On the Non-Negativity of Solutions of the Heat Equation,n

摘要

It is shown that non-negativity of the solution of the heat equation, given non-negative initial values, and suitable boundary conditions, can be established quite readily once the existence of a solution of the equation depending continuously upon the initial values was demonstrated. It is shown that this property is trivially true for the solution of the appropriate finite difference approximation to the partial differential equation, and that the convergence of the solution of the finite difference equation to the solution of the original equation is quite simple, under the above conditions. (Author)