| Abstract: |
| We consider doubly nonlinear parameter-dependent evolution equations (DP;$w,f$) governed by time-dependent subdifferentials in $ V^*$. Here, $V$ is a uniformly convex Banach space such that $V$ is dense in a real Hilbert space $H$ and the injection from $V$ into $H$ is compact. We also suppose that the dual space $V^*$ of $V$ is uniformly convex, and $H=H^*$. Note that our equation (DP;$w,f$) has multiple solutions in general. Therefore, the optimal control problem associated with the state equation (DP;$w,f$) is singular.
In this talk, we study the singular optimal control problem (OP) formulated for (DP;$w,f$) with control $(w,f )$. Then, we show the existence of optimal controls for (OP). We also give some applications to nonlinear PDEs with gradient constraint for time-derivatives.
This is a joint work with Nobuyuki Kenmochi (Chiba University, Chiba, Japan) and Ken Shirakawa (Chiba University, Chiba, Japan). |
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