EXACT INTERNAL CONTROLLABILITY FOR THE WAVE EQUATION IN A DOMAIN WITH OSCILLATING BOUNDARY WITH NEUMANN BOUNDARY CONDITION

In this paper, we study the exact controllability of a second order linear evolution equation in a domain with highly oscillating boundary with homogeneous Neumann boundary condition on the oscillating part of boundary. Our aim is to obtain the exact controllability for the homogenized equation. The limit problem with Neumann condition on the oscillating boundary is different and hence we need to study the exact controllability of this new type of problem. In the process of homogenization, we also study the asymptotic analysis of evolution equation in two setups, namely solution by standard weak formulation and solution by transposition method.

High temperature deformation behavior of Nb-1 wt.%Zr alloy

The hot deformation behavior of Nb-1 wt.%Zr alloy was studied using uniaxial compression tests carried out in vacuum to a true strain of 0.6 in the temperature range of 900 to 1700 degrees C and the strain rate range of 3 x 10(-3) to 10 s(-1). The optimum regime of hot workability of Nb-1Zr alloy was determined from the strain rate sensitivity (m) contour plots. A high m of about 02 was obtained in the temperature and strain rate range of 1200-1500 degrees C and 10(-3) to 10(-1) s(-1) and 1600-1700 degrees C and 10(-1) to 1 s(-1). Microstructure of the deformed samples showed features of dynamic recrystallization within the high strain rate sensitivity domain. Compared to the study on Nb-1Zr-0.1C alloy, Nb-1Zr showed a lower flow stress and an optimum hot working domain at lower temperatures. In the 1500 to 1700 degrees C range the apparent activation energy of deformation for Nb-1Zr was 259 kJ mol(-1), the stress exponent 5, and the activation volume about 200 to 700 b(3). (C) 2015 Elsevier Ltd. All rights reserved.