ABSTRACT

The aim of the present paper is to prove the existence result for a class of differential inclusions governed by the difference of two subdifferentials of nonconvex functions in Hilbert spaces. More precisely, by using the Moreau-Yosida regularization, the existence of local solutions for the following differential inclusion $\dot{u}\left(t\right)+\mathrm{\partial }{\mathrm{\Phi }}_1\left(u\right(t\left)\right)-\mathrm{\partial }{\mathrm{\Phi }}_2\left(u\right(t\left)\right)\ni f\left(t\right)\text{ for almost every }t\in [0,T_0],u\left(0\right)=u_0$ is proved, where both functions ${\mathrm{\Phi }}_1$ and ${\mathrm{\Phi }}_2$ are assumed to be primal lower nice uniformly with respect to subgradients.

中文翻译：

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由两个子微分之差控制的非凸演化包含

摘要

本文的目的是证明希尔伯特空间中由非凸函数的两个次微分的差所支配的一类微分包含的存在性结果。更准确地说，通过使用 Moreau-Yosida 正则化，以下微分包含的局部解的存在$\dot{你}\left(吨\right)+\mathrm{\partial }{\mathrm{\Phi }}_1\left(你\right(吨\left)\right)-\mathrm{\partial }{\mathrm{\Phi }}_2\left(你\right(吨\left)\right)\ni F\left(吨\right)\text{ 几乎每一个 }吨\in [0,{吨}_0],你\left(0\right)={你}_0$被证明，其中两个函数${\mathrm{\Phi }}_1$和${\mathrm{\Phi }}_2$假设相对于次梯度均匀地是原始的较低的好。