Research Article
Mathematical Models for Vegetation Fire PropagationExistence and Uniqueness Analysis
Tchiekre Michel Henri Daugny*
,
Aguemon Wiwegnon Uriel-Longin,
Kambire Diopina Gnowille,
Akahoua David Vincent Brou,
Adou Kablan Jerome
Issue:
Volume 11, Issue 1, March 2026
Pages:
1-5
Received:
7 September 2025
Accepted:
9 October 2025
Published:
4 February 2026
DOI:
10.11648/j.ijssam.20261101.11
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Abstract: This work presents a rigorous mathematical study of a vegetation fire propagation model specifically adapted to the Ivorian environmental context, where climatic conditions and vegetation types significantly influence fire dynamics. The model aims to describe the thermal behavior of vegetation during combustion and the spatial spread of fire fronts. We first analyze a nonlinear ordinary differential equation (ODE) governing the temporal evolution of temperature, which captures the essential mechanisms of heat production and dissipation during combustion. Using classical results from the theory of differential equations, we establish the existence and uniqueness of solutions under suitable assumptions on the model parameters and initial conditions. The study is then extended to a transport-reaction partial differential equation (PDE) that incorporates spatial effects and allows the description of fire propagation in a heterogeneous domain. This PDE model accounts for both the advective transport of heat and the local reaction terms associated with combustion processes. The analysis relies on tools from functional analysis, including appropriate function spaces and a priori estimates, combined with the method of characteristics to handle the transport component of the equation. Under physically relevant assumptions, we prove the existence and uniqueness of weak solutions to the PDE model. The proposed mathematical framework provides a solid theoretical foundation for vegetation fire modeling in West African environments. Beyond its theoretical interest, this work contributes to a better understanding of fire dynamics and offers a basis for future numerical simulations and risk assessment tools aimed at improving fire prevention and management strategies in Côte d'Ivoire and similar regions.
Abstract: This work presents a rigorous mathematical study of a vegetation fire propagation model specifically adapted to the Ivorian environmental context, where climatic conditions and vegetation types significantly influence fire dynamics. The model aims to describe the thermal behavior of vegetation during combustion and the spatial spread of fire fronts...
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Research Article
Integration of Academic Posters as an Active Learning Strategy in Mathematics
Fernando José Hernández Gómez*,
Teresa Hernández Castillo
Issue:
Volume 11, Issue 1, March 2026
Pages:
6-23
Received:
14 August 2025
Accepted:
4 October 2025
Published:
16 March 2026
DOI:
10.11648/j.ijssam.20261101.12
Downloads:
Views:
Abstract: This study presents the outcomes of a pedagogical intervention conducted at the Keiser University during the 2024 − 2025 academic cycle, focusing on the integration of academic posters as an active learning strategy within higher education mathematics instruction. Grounded in constructivist theories and didactic approaches that foster active learner engagement, the intervention aimed to deepen students’ understanding of algebraic concepts through the contextualization of mathematical theory in socially and environmentally relevant phenomena. Empirical data reveal a 15% improvement in algebraic achievement alongside a 30% reduction in mathematics anxiety, thereby demonstrating the effectiveness of the approach in facilitating the internalization of both abstract and procedural mathematical knowledge. The incorporation of contextualized content enabled a significant shift from rote memorization towards reasoning, mathematical argumentation, and modeling. These pedagogical shifts promoted the development of critical skills, mathematical communication, and cooperative competencies-attributes essential for contemporary learning environments. The employment of academic posters as multimodal visual artifacts enhances the externalization of algebraic representations, supporting the construction of mathematically meaningful knowledge applicable to real-world contexts and strengthening the link between theoretical modeling and practical application. These findings emphasize the potential of innovative didactic strategies to bolster formative processes oriented toward systems thinking and social responsibility, positioning mathematics as a visual, argumentative, and propositional discipline. The research validates academic posters as effective tools for situated instruction, enhancing mathematical literacy, curricular innovation, and socio-cognitive skills in higher education.
Abstract: This study presents the outcomes of a pedagogical intervention conducted at the Keiser University during the 2024 − 2025 academic cycle, focusing on the integration of academic posters as an active learning strategy within higher education mathematics instruction. Grounded in constructivist theories and didactic approaches that foster active learne...
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