Zelellou, KheireddineRouar, Salim2021-11-072021-11-072021http://hdl.handle.net/123456789/11256This memory is devoted to the study of reaction-diffusion systems which are systems of partial differential equations of the parabolic type. Reaction-diffusion systems have many applications in various sciences, in particular in the field of biology. This study involves two essential problems, the first problem is the study of the existence of local and global solutions, as well as the explosion of solutions in finite time. We use for this the principle of the fixed point theorem, as well as well chosen test functions. While, the secondproblem is the study of the synchronization problem of reaction-diffusion type systems which have applications in biology using the Layaponuv stability theory.enLocal existanceFixed point theoremReactionComplete synchronizationOther