ABSTRACT
This paper is concerned with the well-posedness of a diffusion–reaction system for a susceptible-exposed-infected-recovered (SEIR) mathematical model. This model is written in terms of four nonlinear partial differential equations with nonlinear diffusions, depending on the total amount of the SEIR populations. The model aims at describing the spatio-temporal spread of the COVID-19 pandemic and is a variation of the one recently introduced, discussed, and tested in a paper by Viguerie et al (2020). Here, we deal with the mathematical analysis of the resulting Cauchy–Neumann problem: The existence of solutions is proved in a rather general setting, and a suitable time discretization procedure is employed. It is worth mentioning that the uniform boundedness of the discrete solution is shown by carefully exploiting the structure of the system. Uniform estimates and passage to the limit with respect to the time step allow to complete the existence proof. Then, two uniqueness theorems are offered, one in the case of a constant diffusion coefficient and the other for more regular data, in combination with a regularity result for the solutions. © 2023 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd.
ABSTRACT
This paper analyzes the constitution of being a teacher in the context of the Covid-19, aiming to: i. characterize the elements present in the process of reframing the teaching professional identity in the context of a pandemic;ii. identify the challenges experienced in professional practice as a teacher in remote education. It is about a descriptive-analytical study of an exploratory nature, related to a more extensive research-intervention, considering the pandemia first year. Focuses on the experience of eight non-remote experienced schoolteachers who act as mentors at referred investigation-intervention. The data comprised written narratives recorded in reflective diaries, virtual activities and, reports by WhatsApp. As a complement, we will consider the deposits of experienced professors registered in virtual synchronous online meetings. It was possible to identify/understand: i. signs of anguish and helplessness when facing the professional effects caused by the pandemic, ii. sense of emptying one's professional identity and iii. challenges in projecting teaching in remote education. It was observed that is this new scenario caused by the pandemic, teachers are going through processes similar to those of beginners who accompany in mentoring, experiencing tensions such as: fear and uncertainty about the future (including the return of regular classroom activities), anxiety, anguish, feeling of incapacity, doubts about the reorganization of school activities (remotely), difficulties in dialogue with the students' family members, concern about children and their families, lack of information and dialogue in schools and education networks, revolt at government actions, among others. It was also observed that new meanings are being attributed to the process of becoming a teacher. The imbalance in the constitution of professional identity was noticed as one of the first effects of the pandemic. Such an imbalance gave way to the empowerment of the teaching identity itself, also causing an expansion of the repertoire of professional knowledge. © 2023, Universidade Estadual de Maringa. All rights reserved.