Approximate controllability and lack of controllability to zero of the heat equation with memory

In this paper we consider the heat equation with memory in a bounded region $\Omega \subset\mathbb{R}^d$, $d\geq 1$, in the case that the propagation speed of the signal is infinite (i.e. the Colemann-Gurtin model). The memory kernel is of class $C^1$. We examine its controllability properties both under the action of boundary controls or when the controls are distributed in a subregion of $\Omega$. We prove approximate controllability of the system and, in contrast with this, we prove the existence of initial conditions which cannot be steered to hit the target $0$ in a certain time $T$, of course when the memory kernel is not identically zero. In both the cases we derive our results from well known properties of the heat equation

Inverse design technique for cascades

A numerical technique to generate cascades is presented. The basic prescribed parameters are: inlet angle, exit pressure, and distribution of blade thickness and lift along a blade. Other sets of parameters are also discussed. The technique is based on the lambda scheme. The problem of stability of the computation as a function of the prescribed set of parameters and the treatment of boundary conditions is discussed. A one dimensional analysis to indicate a possible way for assuring stability for any two dimensional calculation is provided

New insight into the Pleistocene deposits of Monte delle Piche, Rome, and remarks on the biochronology of Hippopotamus (Mammalia, Hippopotamidae) and Stephanorhinus etruscus (Mammalia, Rhinocerotidae) in Italy

Several large mammal assemblages have been collected in the Roman basin since the XIX century, but they usually lack any stratigraphic datum or details about the fossiliferous localities. In this work, the stratigraphic provenance of large mammal remains discovered at Monte delle Piche (Rome) is investigated. The systematic revision of these specimens allows the recording of the presence of Hippopotamus sp., Stephanorhinus sp. and Stephanorhinus etruscus. On the basis of micropalaeontological analysis performed on sediment sampled from the studied specimens and considering the stratigraphy of the area, two fossiliferous levels are recognised at Monte delle Piche. The remain of the hippopotamus was collected in fluvial gravels and sand deposits, in which the presence of Cyprideis is also recorded. This deposit is chronologically related to the latest Early-early Middle Pleistocene. Hippopotamus was present in Italy and Western Europe from the latest Villafranchian to MIS 4/3. The mandible of S. etruscus was collected in marine deposits along with abundant foraminifera and ostracods, which correlate with the late Early Pleistocene. Stephanorhinus etruscus occurred in Western Europe at the beginning of the Villafranchian, and it was documented until the end of the Villafranchian in Italy and until the Early-Middle Pleistocene transition in the Iberian Peninsula

Controllability of a viscoelastic plate using one boundary control in displacement or bending

In this paper we consider a viscoelastic plate (linear viscoelasticity of the Maxwell-Boltzmann type) and we compare its controllability properties with the (known) controllability of a purely elastic plate (the control acts on the boundary displacement or bending). By combining operator and moment methods, we prove that the viscoelastic plate inherits the controllability properties of the purely elastic plate

Boundary Controllability and Observability of a Viscoelastic String

In this paper we consider an integrodifferential system, which governs the vibration of a viscoelastic one-dimensional object. We assume that we can act on the system at the boundary and we prove that it is possible to control both the position and the velocity at every point of the body and at a certain time $T$, large enough. We shall prove this result using moment theory and we shall prove that the solution of this problem leads to identify a Riesz sequence which solves controllability and observability. So, the result as presented here are constructive and can lead to simple numerical algorithms