Thierry Gallouët was a professor of mathematics at the University of Chambéry (1985–1993), the École Normale Supérieure de Lyon (1993–1997), and the University of Aix-Marseille (1997–2023). A specialist in functional analysis and partial differential equations, particularly in the L1 theory of elliptic and parabolic equations, he later became interested in the numerical resolution of partial differential equations with applications in petroleum and hydraulic engineering. Along with Robert Eymard, he pioneered a general theory of the finite volume method.Raphaèle Herbin is a professor of mathematics at the University of Aix-Marseille. She specializes in numerical analysis, particularly in the discretization of partial differential equations. She has contributed to the mathematical analysis of finite volume schemes and their application to various fields, such as electrochemistry and fluid mechanics.

• 1 Sobolev Spaces.- 2 Linear Elliptic Problems.- 3 Quasi-Linear Elliptic Problems.- 4 Parabolic Problems.- 5 Hyperbolic Problems.

Thierry Gallouët was a professor of mathematics at the University of Chambéry (1985–1993), the École Normale Supérieure de Lyon (1993–1997), and the University of Aix-Marseille (1997–2023). A specialist in functional analysis and partial differential equations, particularly in the L1 theory of elliptic and parabolic equations, he later became interested in the numerical resolution of partial differential equations with applications in petroleum and hydraulic engineering. Along with Robert Eymard, he pioneered a general theory of the finite volume method.Raphaèle Herbin is a professor of mathematics at the University of Aix-Marseille. She specializes in numerical analysis, particularly in the discretization of partial differential equations. She has contributed to the mathematical analysis of finite volume schemes and their application to various fields, such as electrochemistry and fluid mechanics.

• 1 Sobolev Spaces.- 2 Linear Elliptic Problems.- 3 Quasi-Linear Elliptic Problems.- 4 Parabolic Problems.- 5 Hyperbolic Problems.