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...

The modelling of the thermal process is used as a tool in determination properties materials, subject to welding. One most important steps calibration heat source model. This necessary condition for given model be solve practical problems. standard practice this regard calibrate by shape melted zone or temperature cycles at set points. In present work, based on maximum temperatures measured sev...

In this paper, we will explore the properties of the Heat Equation on Discrete Networks, laying out groundwork and giving general forms for solutions, and then exploring the inverse problem. We will also focus on comparisons of Heat Networks with Electrical and Random-Walk Networks.

Scale spaces allow us to organize, compare and analyse differently sized structures of an object. The linear scale space of a monochromatic image is the solution of the heat equation using that image as an initial condition. Alternatively, this linear scale space can also be obtained applying Gaussian filters of increasing variances to the original image. In this work, we compare (by looking at...