Inequality of ODE
Suppose $u(t)>0$ satisfies following inequality, how do we solve $u$?
$$u^{'}(t)leq a cdot u^{frac{n+2}{n}}(t)$$
for $tgeq 0$. This seems a little different from Gronwall's inequality, how do we find inequality of $u(t)$, you can add some conditions to $u$ if you want. Thanks for any help.
differential-equations
asked 9 hours ago
STUDENT
886
add a comment |
Suppose $u(t)>0$ satisfies following inequality, how do we solve $u$?
$$u^{'}(t)leq a cdot u^{frac{n+2}{n}}(t)$$
for $tgeq 0$. This seems a little different from Gronwall's inequality, how do we find inequality of $u(t)$, you can add some conditions to $u$ if you want. Thanks for any help.
differential-equations
asked 9 hours ago
STUDENT
886
2
$frac{du}{u^{frac{n+2}{n}}}le a dtto frac 12 n u^{-frac 2n}le a t + C_0$
– Cesareo
6 hours ago
add a comment |
Suppose $u(t)>0$ satisfies following inequality, how do we solve $u$?
$$u^{'}(t)leq a cdot u^{frac{n+2}{n}}(t)$$
for $tgeq 0$. This seems a little different from Gronwall's inequality, how do we find inequality of $u(t)$, you can add some conditions to $u$ if you want. Thanks for any help.
differential-equations
asked 9 hours ago
STUDENT
886
Suppose $u(t)>0$ satisfies following inequality, how do we solve $u$?
$$u^{'}(t)leq a cdot u^{frac{n+2}{n}}(t)$$
for $tgeq 0$. This seems a little different from Gronwall's inequality, how do we find inequality of $u(t)$, you can add some conditions to $u$ if you want. Thanks for any help.
differential-equations
differential-equations
asked 9 hours ago
STUDENT
886
asked 9 hours ago
STUDENT
886
asked 9 hours ago
STUDENT
886
asked 9 hours ago
STUDENT
886
asked 9 hours ago
STUDENT
886
886
2
$frac{du}{u^{frac{n+2}{n}}}le a dtto frac 12 n u^{-frac 2n}le a t + C_0$
– Cesareo
6 hours ago
add a comment |
2
$frac{du}{u^{frac{n+2}{n}}}le a dtto frac 12 n u^{-frac 2n}le a t + C_0$
– Cesareo
6 hours ago
2
2
$frac{du}{u^{frac{n+2}{n}}}le a dtto frac 12 n u^{-frac 2n}le a t + C_0$
– Cesareo
6 hours ago
$frac{du}{u^{frac{n+2}{n}}}le a dtto frac 12 n u^{-frac 2n}le a t + C_0$
– Cesareo
6 hours ago
add a comment |
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2
$frac{du}{u^{frac{n+2}{n}}}le a dtto frac 12 n u^{-frac 2n}le a t + C_0$
– Cesareo
6 hours ago