In this paper, we consider a transmission problem for a system of a thermoelastic plate with (or without) rotational inertia term coupled with a membrane with different variants of damping for the plate and/or the membrane. We prove well-posedness of the problem and higher regularity of the solution and study the asymptotic behavior of the solution, depending on the damping and on the presence of the rotational term.

In this paper, we consider a transmission problem for a system of a thermoelastic plate with (or without) a rotational inertia coupled with a membrane. On the plate a structural damping may or may not act, and on the membrane a damping of Kelvin–Voigt type may or may not be present; free boundary operators for the plate are considered in the coupling with the membrane. We prove well‐posedness of the problem and higher regularity of the solution. Depending on the damping and on the presence of the rotational term, we establish strong stability, exponential stability, lack of exponential stability, polynomial stability, and analyticity of the semigroup associated to the transmission problem.

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We consider Fourier multiplier systems on Rn with components belonging to the standard Hörmander class S1,0mRn, but with limited regularity. Using a notion of parameter-ellipticity with respect to a subsector Λ⊂C (introduced by Denk, Saal, and Seiler) we show the generation of both C∞ semigroups and analytic semigroups (in a particular case) on the Sobolev spaces WpkRn,Cq with k∈N0, 1≤p<∞ and q∈N. For the proofs, we modify and improve a crucial estimate from Denk, Saal and Seiler, on the inverse matrix of the symbol (see Lemma ). As examples, we apply the theory to solve the heat equation, a linear thermoelastic plate equation, a structurally damped plate equation, and a generalized plate equation, all in the whole space, in the frame of Sobolev spaces.

In the academic world and more specifically in engineering education programmes, the aim is to develop teaching activities, which promote the achievement of formal thought in students. Cognitive theories insist that knowledge is meaningful and therefore opinions of students about themselves and their environment should be considered. Consequently, professors need to take into account how mental processes are manifested during learning. PURPOSE OR GOALThis work aims to measure and detect significant changes in the scientific reasoning skills of university engineering students. In particular, it wants to determine if the curriculum map of courses belonging to the core of mathematics and physics, which is typically seen in the first two years of the curriculum of engineering programmes, contributes significantly to the academic education and learning of students APPROACH OR METHODOLOGY/METHODS A case study was developed in the College of Engineering of the Universidad del Norte. It was composed of two important chronological stages. Stage 1: In the first semester of 2015, it was applied the modified LCTSR to all students who will complete their first semester in the engineering programmes (more than 800 students). Stage 2: In the first semester of 2017, the same test was applied to a large group of students. As a result, it was obtained that 126 students presented the same LCTSR in both 2015 and 2017. The exposed analyses seek to answer the following two questions: i)Has basic sciences education contributed to the development and enhancement of formal thinking in Engineering students?, ii)Is there a correlation between the academic performance of students and the thought stage measured to students through the Lawson Classroom Test of Scientific Reasoning (LCTSR)? ACTUAL OR ANTICIPATED OUTCOMES These descriptive results indicate that even when there was an improvement in 2017, this improvement does not seem to be large enough for most students to develop formal thinking.It should be taken into consideration that in 2017 at least 40% of students are still under 19 years old. Also, the results supported the idea that there is a positive correlation between the LCTSR score and the academic performance of students CONCLUSIONS/RECOMMENDATIONS/SUMMARY On average, the training received by the students from Engineering programmes in the core courses of mathematics and physics, actually develops their logical thinking/reasoning skills. However, these seem not to be sufficient for students to show an ideal academic performance in the basic core courses of engineering programmes. Finally, the overall results of this study show an opportunity for improvement in engineering programs.