Summary: This series of minicourses explores both the analytical and numerical aspects of partial differential equations in applied contexts. The first minicourse examines transport equations in structured population dynamics, focusing on the renewal model for age-structured populations. Global existence, well-posedness, and long-term behavior of solutions will be discussed, as well as extensions such as the McKendrick–Von Foerster and growth–fragmentation models with applications to cell division and oncology. The second minicourse introduces the finite volume discretization of elliptic equations under various boundary conditions (Dirichlet, flux, Robin). Starting with the Two-Point Flux Approximation (TPFA) for stationary problems, the framework is extended to convection–diffusion and unsteady equations, including the heat and Fisher–KPP equations, with numerical illustrations using the Python library pynitevolume developed by the team in Marseille. Together, the minicourses provide a combined theoretical and computational perspective, equipping participants with analytical tools for studying structured biological models and practical techniques for implementing finite volume methods in applied PDEs. 

Prior to the course, Patrick Tchepmo Djomegni will deliver a minicourse on hyperbolic PDEs and laws conservation. The minicourse will introduce and discuss key concepts, including the method of characteristics, classical solutions, weak solutions, entropy solutions, as well as shock and rarefaction waves.

Invited lecturer: Florence Hubert (Aix-Marseille University, France)

Contact: math.mod.mc@gmail.com 

Registration deadline: 15 January 2026

Organizing committee:

• Patrick M Tchepmo Djomegni (North-West University, South Africa)

• Sanne ter Host (North-West University, South Africa)

• Cedric I Hameni Nkwayep (North-West University, South Africa)

• Fundile Nyaweni (Nelson Mandela University, South Africa)

• Franc Kgomotshwana Thosago (University of Limpopo, South Africa)

• Umida Baltaeva (Urgench State University, Uzbekistan)

Scientific committee:

• Sophie Dabo-Niang (University of Lille, France)

• Sanne ter Host (North-West University, South Africa)

• Florence Hubert (Aix-Marseille University, France) 

• Patrick M Tchepmo Djomegni (North-West University, South Africa)

• Stephanie Portet (University of Manitoba, Canada)