Numerical resolution of an exact heat conduction model with a delay term

In this paper we analyze, from the numerical point of view, a dynamic thermoelastic problem. Here, the so-called exact heat conduction model with a delay term is used to obtain the heat evolution. Thus, the thermomechanical problem is written as a coupled system of partial differential equations, and its variational formulation leads to a system written in terms of the velocity and the temperature fields. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, from which the linear convergence of the algorithm could be derived under suitable additional regularity conditions. Finally, a two-dimensional numerical example is solved to show the accuracy of the approximation and the decay of the discrete energy.Peer ReviewedPostprint (published version

Optimization of a low weight electronic differential for LEVs

It is presented a performance analysis of an Electronic Differential (ED) system designed for Light Electric Vehicles (LEVs). We have developed a test tricycle vehicle with one front steering wheel and two rear fixed units is a same axis with a brushless DC integrated in each of them. Each motor has an independent controller unit and a common Arduino electronic CPU based that can plan specific speeds for each wheels as curves are being traced. Different implementations of sensors (input current/torque, steering angle and speed of the wheels) are discussed related to hardware complexity, and performance obtained based on speed level requirements and slipping on the traction wheels.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Anisotropy can imply exponential decay in micropolar elasticity

In this note, two problems arisen in micropolar elasticity are considered from the analytical point of view. Following the Kelvin–Voigt theory of micropolar viscoelasticity, two dissipative mechanisms are imposed: in the first problem, it is defined on the microscopic structure and, for the second problem, on the macroscopic structure. Then, an existence and uniqueness result, as well as an exponential energy decay, are proved for the first problem. Since similar arguments can be used for the second problem, only the main key points are commented.Agencia Estatal de Investigación | Ref. PID2019-105118GB-I00Universidade de Vigo/CISU

On the time decay for an elastic problem with three porous structures

In this paper, we study the three-dimensional porous elastic problem in the case that three dissipative mechanisms act on the three porosity structures (one in each component). It is important to remark that we consider the case when the material is not centrosymmetric, and therefore, some coupling, not previously considered in the literature concerning the time decay of solutions in porous elasticity, can appear in the system of field equations. The new couplings provided in this situation show a strong relationship between the elastic and the porous components of the material. In this situation, we obtain an existence and uniqueness result for the solutions to the problem using the Lumer-Phillips corollary to the Hille-Yosida theorem. Later, assuming a certain condition determining a “very strong” coupling between the material components, we can use the well-known arguments for dissipative semigroups to prove the exponential stability of the solutions to the problem. It is worth emphasizing that the proposed condition allows bringing the decay of the dissipative porous structure of the problem to the macroscopic elastic structure.Agencia Estatal de Investigación | Ref. PID2019-105118GB-I00Universidade de Vigo/CISU

Uniqueness for a high order ill posed problem

In this work, we study a high order derivative in time problem. First, we show that there exists a sequence of elements of the spectrum which tends to infinity and therefore, it is ill posed. Then, we prove the uniqueness of solutions for this problem by adapting the logarithmic arguments to this situation. Finally, the results are applied to the backward in time problem for the generalized linear Burgers’ fluid, a couple of heat conduction problems and a viscoelastic model.Agencia Estatal de Investigación | Ref. PGC2018-096696-B-I00Agencia Estatal de Investigación | Ref. PID2019-105118GB-I0

Fast spatial behavior in higher order in time equations and systems

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGIn this work, we consider the spatial decay for high-order parabolic (and combined with a hyperbolic) equation in a semi-infinite cylinder. We prove a Phragmén-Lindelöf alternative function and, by means of some appropriate inequalities, we show that the decay is of the type of the square of the distance to the bounded end face of the cylinder. The thermoelastic case is also considered when the heat conduction is modeled using a high-order parabolic equation. Though the arguments are similar to others usually applied, we obtain new relevant results by selecting appropriate functions never considered before.Agencia Estatal de Investigación | Ref. PGC2018-096696-B-I00Agencia Estatal de Investigación | Ref. PID2019-105118GB-I0

n-coupling mechanisms are sufficient to obtain exponential decay in strain gradient elasticity

In this paper, we consider the time decay of the solutions to some problems arising in strain gradient thermoelasticity. We restrict to the two-dimensional case, and we assume that two dissipative mechanisms are introduced, the temperature and the mass dissipation. First, we show that this problem is well-posed proving that the operator defining it generates a contractive semigroup of linear operators. Then, assuming that the function involving the coupling terms is elliptic, the exponential decay of the solutions is concluded as well as the analyticity of the solutions. Finally, we describe how to obtain the exponential stability in the case of hyperbolic dissipation.Agencia Estatal de Investigación | Ref. PID2019-105118GB-I00Universidade de Vigo/CISU

On the thermoelasticity with several dissipative mechanisms of type III

It is accepted that we cannot obtain the exponential decay of the solutions to the type III thermoelasticity when the dimension of the domain is greater than one. In this short note, we prove that we can show the exponential decay if we consider type III dissipative mechanisms whenever the coupling terms satisfy a certain condition.Agencia Estatal de Investigación | Ref. PID2019-105118GB-I00Universidade de Vigo/CISU