| Abstract: |
| We consider the following nonlinear evolution equation in a real Hilbert space.
$$
\frac{du}{dt}(t) + \partial \varphi (u (t) )
+ B(t , u (t) ) \ni f (t )
~~~~t \in [0, T],
$$
where $\partial \varphi $ is the subdifferential operator generated by a proper lower semi-continuous convex functional $\varphi $, $B$ is a perturbation term, and $f$ is a given external force.
When $B \equiv 0$, it is well known that the right-differentiability of $u$ at $t _ 0 \in [0, T ]$ is equivalent to the property that $u (t _ 0) $ belongs to the domain of $\partial \varphi $.
This is a useful tool for establishing higher order estimates in the analysis of evolution equations.
In this talk, we give a sufficient condition of perturbation $B$ to obtain the same characterization of right-differentiability as above. |
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