We consider the inverse problem of finding the temperature distribution and the heat source whenever the temperatures at the initial time and the final time are given. The problem considered is one dimensional and the unknown heat source is supposed to be space dependent only. The existence and uniqueness results are proved.

We consider the inverse source problem for a time fractional diffusion equation. The unknown source term is independent of the time variable, and the problem is considered in two dimensions. A biorthogonal system of functions consisting of two Riesz bases of the space L2[(0,1) × (0,1)], obtained from eigenfunctions and associated functions of the spectral problem and its adjoint problem, is used to represent the solution of the inverse problem. Using the properties of the biorthogonal system of functions, we show the existence and uniqueness of the solution of the inverse problem and its continuous dependence on the data. Copyright © 2012 John Wiley & Sons, Ltd.

Bluetooth Low Energy (BLE) represents the low-power, low-cost extension of the Bluetooth communication technology envisioned for the Internet of Things. Mesh protocols on top of BLE are currently emerging and the standard is currently being released. This paper first proposes a detailed measurement based comparison of two mesh approaches that fit within BLE operation: flooding and connection oriented networking. Using metrics such as packet delivery ratio (PDR), end-to-end delay and power consumption we conclude that the optimal mesh approach depends on the application. It is shown that for a comparable performance in terms of PDR and overhead, flooding can trade a lower end-to-end delay for a higher power consumption when compared to the connected mesh. We then propose an architecture, called Bluetooth Now, that is able to automatically switch the network between the two based on message priority. Our measurement results confirm the reliable delivery of important and urgent data sent using the Bluetooth Now paradigm, while saving battery life when transmitting non-time critical messages.