Strong asymptotic convergence of evolution equations governed by maximal monotone operators

We consider the Tikhonov-like dynamics $-\dot u(t)\in A(u(t))+\varepsilon(t)u(t)$ where $A$ is a maximal monotone operator and the parameter function $\eps(t)$ tends to 0 for $t\to\infty$ with $\int_0^\infty\eps(t)dt=\infty$. When $A$ is the subdifferential of a closed proper convex function $f$, we establish strong convergence of $u(t)$ towards the least-norm minimizer of $f$. In the general case … Read more

Asymptotic equivalence and Kobayashi-type estimates for nonautonomous monotone operators in Banach spaces

We provide a sharp generalization to the nonautonomous case of the well-known Ko\-ba\-yashi estimate for proximal iterates associated with maximal monotone operators. We then derive a bound for the distance between a continuous-in-time trajectory, namely the solution to the differential inclusion $\dot{x} + A(t)x\ni 0$, and the corresponding proximal iterations. We also establish continuity properties … Read more