We consider an optimal boundary control problem for a one-dimensional wave equation consisting of two non-homogenous segments with piecewise constant characteristics. The describes the longitudinal vibrations non-homogeneous rod or transverse string given initial, intermediate, and final conditions. assume that travel time each sections is same. carried out by shifting one end other fixed. qual...

We consider an inverse problem of determining a spatially varying factor in a source term in a nonstationary linearized Navier-Stokes equations by observation data in an arbitrarily fixed sub-domain over some time interval. We prove the Lipschitz stability provided that the t-dependent factor satisfies a non-degeneracy condition. Our proof based on a new Carleman estimate for the Navier-Stokes ...