BV periodic solutions of an evolution problem associated with continuous moving convex sets
BV periodic solutions of an evolution problem associated with continuous moving convex sets
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与连续移动凸集相关的演化问题的 BV 周期解
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
M. Marques
中科院分区：
文献类型：
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作者：
C. Castaing;M. Marques
本文研究了由扫掠过程（或莫罗过程）控制的演化方程的多值扰动的BV周期解。扰动方程的形式为- Du∈NC(t)(u(t))+F(t,u(t))，其中c是一个闭合凸值连续周期多函数，从[0，t]到F(t)， NC(t)（u(t)）是c (t)在u(t)上的法锥，F: [0, t]× F（d→l）是一个紧凸值多函数，Du是周期BV解u的微分测度。在不同的摄动条件下，给出了该微分包涵的几个存在性结果。
This paper is concerned with BV periodic solutions for multivalued perturbations of an evolution equation governed by the sweeping process (or Moreau's process). The perturbed equation has the form −Du∈NC(t)(u(t))+F(t,u(t)), whereC is a closed convex valued continuousT-periodic multifunction from [0,T] to ℝd,NC(t)(u(t)) is the normal cone ofC(t) atu(t),F: [0,T]×ℝd→ℝd is a compact convex valued multifunction and Du is the differential measure of the periodic BV solutionu. Several existence results for this differential inclusion are stated under various assumptions on the perturbationF.