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A new tag . It now has 10 question. It has a tag-excerpt: "Questions on inequalities similar to the classical Gronwall's lemma. Typically, a function's derivative is bounded by (some variation of) itself. This may also be given in the corresponding integral version instead. From there an estimate for the original function can be derived"
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Recently, I needed some generalized version of Gronwall's Lemma, which I couldn't find in a quick search. However, I discovered that MSE is full of questions differing only in details on this very topic. Hence, I was wondering if there is a general version of Gronwall's inequality which covers mo...

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Is there a Gronwall-type inequality for bounding $u(t)$ such that $$\vert \partial_t u(t)\vert\leq C \{ u(t)+u(t)^\alpha\}$$ with $\alpha>1$ ?

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This question concerns a proof of a theorem involving Gronwall type inequality. We have the following: The question is: how did we apply Gronwall type inequality to get estimate (3.6)?

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Suppose a (continuous, non-negative) function $f$ satisfies $$f'(t) \leq f(t)^2$$ for $t \in [0,1]$. Set $$g(t) = \exp\left(-\frac{1}{f(t)}\right).$$ Then $$g'(t) = \frac{f'(t)}{f(t)^2} g(t) \leq g(t),$$ so applying the standard Gronwall inequality one has $g(t) \leq g(0) e^t$. Since $\log... 2 I want to derive a Gronwall-type inequality from the inequality below. Here all the functions are nonnegative, continuous and if you need some assumptions you may use that. $$f^2(t) \leqslant g^2(t) + \int_0^t (f(s) +c) f(s) ds \;\;\;\; (t \in [0,T])$$ So please help! 0 I am looking for a proof or refrence for the following Gronwall-type inequality: Let$ \varphi (t,s) $is a continous function for$0 \leq s < t \leq T$. If the following inequality holds: $$\varphi (t,s) \leq A + B \int_s^t ( t - \sigma)^{\alpha -1} \varphi ( \sigma , s) d \sigma$$ for som... 2 Let$u: (0,\infty) \times \mathbb R \to \mathbb R$. Suppose that$\int_{\mathbb R} u(t,x) dx \ge 0$(but not necessarily$u >0$). Let$A:(0,\infty) \to \mathbb R$with$A \ge 0$. Let$\alpha \ge 0$. Suppose that we know $$\frac{d}{dt} \alpha\int_{\mathbb R} u(t,x) dx + A(t) \le \int_{\mathbb R}... 2 Does somebody knows if it is possible to obtain an inequality (like for Gronwall inequality) on f if f verify$$ f(t) \leq A+\int_0^{2t} g(s)f(s) ds $$. Where f and g are as smooth as necessary and nonnegative. Thanks. 35 The Gronwall lemma is a well known and very useful statement which is used in many situations, in particular in the theory of differential equations. I have seen it so many times and even the proof is very easy to understand. But at the end of the day it is seems to me a very technical 'thing', I... 1 I would like to know if there is any kind of Gronwall inequality for a smooth function u \colon \mathbb{R}^n \to \mathbb{R} satisfying$$ |\nabla u | \le K u,$$where$K\$ is a constant.

In mathematics, Grönwall's inequality (also called Grönwall's lemma or the Grönwallâ€“Bellman inequality) allows one to bound a function that is known to satisfy a certain differential or integral inequality by the solution of the corresponding differential or integral equation. There are two forms of the lemma, a differential form and an integral form. For the latter there are several variants. Grönwall's inequality is an important tool to obtain various estimates in the theory of ordinary and stochastic differential equations. In particular, it provides a comparison theorem that can be used to...
At some point there was a tag called , but it was removed quickly after it was created. math.stackexchange.com/posts/1131077/revisions chat.stackexchange.com/transcript/3740/2016/5/25
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Resolved: Tag has been removed. I was going to remove the tag gronwall-inequality from this question until I realized that there were a hundred questions related to this inequality. I am not too familiar with DEs: do people who are think this could use a tag?

I've heard colleagues mention it multiple times and I've seen it in stochastic processes. I think it's probably safe to leave it as is. I think people who need it, it's a very good tag to have. — Cameron Williams Feb 3, 2015 at 5:22
Right, so I guess my question is whether it is worth creating tagging those 100 questions. — Eric Stucky Feb 3, 2015 at 5:30
Oh I see. I totally had the opposite understanding of your comment. I feel silly now. Reading comprehension is hard. I think it might be beneficial for sure. — Cameron Williams Feb 3, 2015 at 5:32