Simulation of extensive air shower at energies of Pierre Auger observatory and lateral distribution function

The Pierre Auger Observatory is the largest experiment ever designed to detect ultra high energy cosmic-rays. Its large area must allow to obtain statistics for energies above 10¹⁹ eV to understand their origin. The Hybrid mode of detection provide accuracy on primary energy reconstruction and on the arrival direction. In the first chapter, we present the history of cosmic rays and the problems occurring at ultra high energy. In a second part, the detectors of the Pierre Auger Observatory are presented, with motivations and constraints of the installation on the site. In the third part, we describe the extensive air shower simulation. We begin by the first interaction at high energy where hadronic models are unknown and have to be extrapolated. Then, we continue the development of the shower with the electromagnetic cascade and the penetrating component which are detected respectively by fluorescence and surface detectors. The chapter four is dedicated to a new lateral distribution function (decreasing of signal in function of distance to the shower core) that we propose. The new function is able to fit the individual shower behaviour and allows a better reconstruction of energy estimators. We test this new function to the engineering array data. Finally, we present the data of engineering array installed in the Pampa and the reconstruction of its events. (author)