Alves, Claudianor O.Boudjeriou, Tahir2022-09-272022-09-2720220022-247Xhttps://www.sciencedirect.com/science/article/pii/S0022247X22005236https://doi.org/10.1016/j.jmaa.2022.126509https://dspace.univ-boumerdes.dz/handle/123456789/10092This paper concerns the existence of global solutions for the following class of heat equations involving the 1-Laplacian operator for the Dirichlet problem {ut−Δ1u=f(u)inΩ×(0,+∞),u=0in∂Ω×(0,+∞),u(x,0)=u0(x)inΩ, where Ω⊂RN is a smooth bounded domain, N≥1, f:R→R is a continuous function satisfying some technical conditions and [Formula presented] denotes the 1-Laplacian operator. The existence of global solutions is done by using an approximation technique that consists in working with a class of p-Laplacian problems associated with (P) and then taking the limit when p→1+ to get our resultsenDegenerate parabolic equationsGalerkin methodsNonlinear parabolic equationsArticle