Journal of Advances in Applied Mathematics

7

Authors: Qingjie Hu, Haiqi Zhang, Yu Chen, Ming Tang

In this paper, by introducing a Fritz-John type result for mathematical program with vanishing constraints (MPVC), we present some new constraint qualifications which are strictly weaker than the MPVC-Mangasarian Fromovitz constraint qualification (MPVC-MFCQ). We show that the MPVC-tailored penalty function which was introduced in [1] is still exact for MPVC under the MPVC-generalized pseudonormality. Our exact penalty result improves the one in [1].

12

Authors: Miaomiao Wang, Weiwei Chang, Xiaojun Li

This paper is devoted to study the long-time behavior of non-autonomous parabolic equation with nonlocal diffusion and hereditary effect, where time symbol is translation bound in L 2 loc(R; H−1 (Ω)) and L 2 loc(R;L 2 (Ω)), respectively. By the energy estimates and asymptotic priori estimates of solutions, we obtain the existence and regularity of uniform attractor for the family of processes corresponding to original systems, respectively.