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This paper investigates first-order variable metric backward forward dynamical systems associated with monotone inclusion and convex minimization problems in real Hilbert space. The operators are chosen so that the backward-forward dynamical system is closely related to the forward-backward dynamical system and has the same computational complexity. We show existence, uniqueness, and weak asymptotic convergence of the generated trajectories and strong convergence if one of the operators is uniformly monotone. We also establish that an equilibrium point of the trajectory is globally exponentially stable and monotone attractor. As a particular case, we explore similar perspectives of the trajectories generated by a dynamical system related to the minimization of the sum of a nonsmooth convex and a smooth convex function. Numerical examples are given to illustrate the convergence of trajectories., Comment: 3 figures

The investigation of creep recovery and stress relaxation in aluminum using a closed loop servo-hydraulic test system is described. The practicality of a computer controlled test system for constant plastic strain rate tension tests is demonstrated. The plastic strain rate and the magnitude of the initial strain are shown to have a noticeable effect on subsequent creep behavior of aluminum.

Creep tests were conducted by means of a closed loop servo-controlled materials test system. These tests are different from the conventional creep tests in that the strain history prior to creep may be carefully monitored. Tests were performed for aluminum alloy 6061-0 at 150 C and monitored by a PDP 11/04 minicomputer at a preset constant plastic-strain rate prehistory. The results show that the plastic-strain rate prior to creep plays a significant role in creep behavior. The endochronic theory of viscoplasticity was applied to describe the observed creep curves. The concepts of intrinsic time and strain rate sensitivity function are employed and modified according to the present observation.