The asynchronous iterations applied to the modified porous medium equation

Abstract : The purpose of this work is to establish the existence and uniqueness of the solution of the porous medium equation where the solution is subject to certain constraints, for the boundary conditions of Dirichlet and resolve it by different numerical methods. After a appropriate change of variables, we consider an implicit time discretization scheme that leads to solve at each time a sequence of nonlinear stationary problems. For each stationary problem, we use a spatial discretization that leads to each time to solve a multivalued large nonlinear algebraic system. Finally, we applied subdomain asynchronous parallel methods without overlapping and we established the convergence by a contraction technique.