A. M. Simões

Integral equation methods in problems of wave diffraction by a strip with higher order reactance conditions

A problem of wave diffraction by a strip characterized with higher order reactance boundary conditions will be analysed from an integral equations viewpoint. The problem will be formulated as a boundary-transmission problem for the Helmholtz equation and in a Bessel potential space setting. Integral equations and operator theoretical methods are used to deal with the problem and, as a consequence, several convolution type equations are constructed and associated to the problem. At the end, the solvability of the problem will be discussed for a range of regularity orders of the Bessel potential spaces.

On the Solvability of a Problem of Wave Diffraction by a Union of a Strip and a Half‐Plane

We consider a problem of wave diffraction by a union of an infinite strip and an half‐plane characterized by higher order boundary conditions. From the mathematical point of view, the problem is formulated as a boundary value problem for the Helmholtz equation within a Bessel potential space framework. Operator theoretical methods are used to deal with this problem and, as a consequence, several convolution type operators are constructed and associated to the problem. A Fredholm characterization of those operators is obtained for certain smoothness space orders.

Fredholm Analysis for a Wave Diffraction Problem with Higher Order Boundary Conditions on a Union of Strips

A problem of wave diffraction by a union of infinite strips characterized by higher order boundary conditions is here analyzed from an operator theory viewpoint. The main goal is to describe when the operators associated with the problem enjoy the Fredholm property. This is done by constructing several operator extension methods between the used convolution type operators. The problem and the operators are defined between Bessel potential spaces, and thus the Fredholm property is obtained for a set of regularity indices of these spaces.

HIGHER EDUCATION METHODOLOGIES: FROM URBAN PLANNING TO MATHEMATICAL ISSUES

This article will be focused on higher education learning and teaching methodologies, based on the experience of the Master Degree in Civil Engineering at the University of Beira Interior, in Covilhã (Portugal). It aims to present the results of the practises used by scholar of urban planning and mathematical issues, both regarding the civil engineering research field. Actually, there are some similarities in between the research process features of urban planning domain and mathematics field in order to promote the students’ success. In fact, these both scientific subjects follow analogous tasks in their research processes, not only regarding the same starting point which is the definition of the research problem, but also observing the final phase, which is based on the findings of results, or the proposed solution. It joins scholars from the department of civil engineering and architecture, experts in spatial analysis and scholars from the department of mathematics of the University of Beira Interior (UBI). One case study will be presented as an example and pioneer research of the application of these methodological approaches. It will be focused on the urban planning experiences, associated with postgraduate teachings. It is related to a PhD thesis in Civil Engineering focused on urban planning issues.

Hyers-Ulam and Hyers-Ulam-Rassias stability of a class of Hammerstein integral equations

The purpose of this paper is to study different kinds of stability for a class of Hammerstein integral equations. Sufficient conditions are derived in view to obtain Hyers-Ulam stability and Hyers-Ulam-Rassias stability for such a class of Hammerstein integral equations. The consequent different cases of a finite interval and an infinite interval are considered, and some concrete examples are included to illustrate the results.