Abstract : This thesis is devoted to a quasilinear parabolic equation in which the diffusion is defined by the length of different nonlocal interactions. As regards stationary problem, having shown the results of existence, uniqueness and continuity. We introduce a general criterion of inversibility later depending on parameter, this very important criterion is going to allow us in example of application to find well known results when parameter will be equal to the diameter of domain. We give then a fundamental result of comparison of solutions in the case of radial symmetrical solutions and a general implementation of count of solutions. Finally we give some numerical applications using a method of fixed point and Newton's method to illustrate these results. As regards parabolic problem having shown existence of global attractor associated to our problem, we show an estimate $L^\infty$ of solution according to estimate $L^q$, $q>1$ by using Moser's iteration.