7
votes
1answer
319 views

About the convergence rate for an approximation to the heat kernel

Let $G(t,x)$ be the heat kernel $$ G(t,x)=\frac{1}{\sqrt{2\pi t}}e^{-\frac{x^2}{2t}}, \quad t>0, \:x\in\mathbb{R}. $$ Here is one approximation to $G(t,x)$: $$ G_\epsilon(t,x)=e^{-t/\epsilon} ...
1
vote
0answers
57 views

Semiflows and continuous symmetries

Given a differential equation on a Banach space $\mathcal{X}$ of the form $\frac{d u}{d t} = F(u)$, it is often the case that $F$ is equivariant under translations, i.e. that $T_\alpha F(u) = ...