The null-controllability property of a 1 − d parabolic equation involving a fractional power of the Laplace operator, (−∆), is studied. The control is a scalar time-dependent function g = g(t) acting on the system through a given space-profile f = f(x) on the interior of the domain. Thus, the control g determines the intensity of the space control f applied to the system, the latter being given...

In this paper, we consider boundary stabilization problem of heat equation with multi-point source. Firstly, a state feedback controller is designed mainly by backstepping approach. Under the controller, exponential stability closed-loop system guaranteed. Then, an observer-based output proposed. We prove resulting using operator semigroup theory. Finally, and controllers are effective via some...

Casting is considered as a major manufacturing process. Thermal analysis of a solidifying medium is of great importance for appropriate design of casting processes. The conventional governing equation of a solidifying medium is based on the Fourier heat conduction law, which does not account for the phase-lag between the heat flux and the temperature gradient. In this paper, the concept of phas...

This paper evaluates the use of the compressible Navier-Stokes equations, with prescribed zero velocities, as a model for heat transfer in solids. In particular in connection with conjugate heat transfer problems. We derive estimates, and show how to choose and scale the coefficients of the energy part in the Navier-Stokes equations, such that the difference between the energy equation and the ...