Let $A$ a linear operator from his domaine $D(A)\subset H$ to $H$, with $H$ is a Hilbert space, such that $A$ is dissipative, and let $B$ is a monotone linear operator such that $D(A)\subset D(B)$.

we suppose that $C=A-B$ gererate a contraction semi group $T(t)$ on $H$; then for all $z_0\in H$ $\frac{dz}{dt}=Cz$ admet a unique solution in H.

Question :

under what conditions we have $t\longrightarrow\|Az(t)\|$ is an increasing function ?

Let $A$ a linear operator from his domaine $D(A)\subset H$ to $H$, with $H$ is a Hilbert space, such that $A$ is dissipative, and let $B$ is a monotone linear operator such that $D(A)\subset D(B)$.

we suppose that $C=A-B$ gererate a contraction semi group $T(t)$ on $H$; then for all $z_0\in H$ $\frac{dz}{dt}=Cz$ admet a unique solution in H.

Question :

under what conditions we have $t\longrightarrow\|Az(t)\|$ is an increasing function ?

Thank you