Chattouh AbdeldjalilSaoudi Khaled2024-02-152024-02-152020http://dspace.univ-khenchela.dz:4000/handle/123456789/1183A semilinear Sobolev equation ∂t(u − ∆u) − ∆u = f(∇u) with a Dirichlet-type integral boundary condition is investigated in this contribution. Using the Rothe method which is based on a semi-discretization of the problem under consideration with respect to the time variable, we prove the existence and uniqueness of a weak solution. Moreover, a suitable approach for the numerical solution based on Legendre spectral-method is presented.enArticle