---
tag: 0ZPQHH37PF
kind: concept
name: Grönwall bound
msc: [34A40]
sources:
  - url: https://en.wikipedia.org/wiki/Gr%C3%B6nwall%27s_inequality
    locator: lead section
---

## Summary

The Grönwall bound is the solution $x \mapsto \delta e^{Kx} + \frac{\varepsilon}{K}(e^{Kx} - 1)$ of $v' = K v + \varepsilon$, $v(0) = \delta$, with the value $\delta + \varepsilon x$ when $K = 0$.
It is the upper bound in a form of [[Grönwall's inequality|07EJHQYR9A]]. See the [[definition|0FRX8JD7QH]].