In this paper we prove the existence of variational solutions to the obstacle problem associated with doubly nonlinear equations $\partial_t (|u|^{m-1}u) - \mathrm {div}(D_\xi f(Du)) = 0$ with $m > 1$ and a convex function $f$ satisfying a standard $p$-growth condition for an exponent $p \in (1,\infty)$ in a bounded space-time cylinder $\Omega_T := \Omega \times (0,T)$. The obstacle function $\psi$ and the boundary values $g$ are time dependent. The proof relies on a nonlinear version of the method of minimizing movements.

中文翻译：

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多孔介质型奇异双非线性方程组的障碍问题

在本文中，我们证明了与双重非线性方程$ \ partial_t（| u | ^ {m-1} u）-\ mathrm {div}（D_ \ xi f（Du））=相关的障碍问题的变分解的存在。 0 $，其中$ m> 1 $，且凸函数$ f $满足有界时空圆柱$ \ Omega_T中指数$ p \ in（1，\ infty）$的标准$ p $-增长条件\ Omega \ times（0，T）$。障碍函数$ \ psi $和边界值$ g $与时间有关。该证明依赖于最小化运动方法的非线性版本。