| Abstract: |
| We consider second order nonlinear quasi-variational evolution inclusions 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 $H=H^*$.
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In this talk, we establish the abstract result on the existence of solutions to our problem by applying the abstract theory of the time-derivative operators and the fixed-point theorem of Schauder type. In addition, we give some applications to nonlinear PDEs with gradient constraint for time-derivatives.
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This is a joint work with Nobuyuki Kenmochi (Chiba University, Chiba, Japan) and Ken Shirakawa (Chiba University, Chiba, Japan). |
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