Taharaoui, RomaissaeTCHOUAR, Fatima Zahra2024-12-112024-12-112023http://dspace.univ-temouchent.edu.dz/handle/123456789/5889This work is devoted to the study of the Cauchy problem within the context of the distribution space. We have explored integrable and regular functions that hold values in a Banach space. Furthermore, we have tackled the concept of distribution semi-groups. In conclusion, we have examined the necessary conditions for the Cauchy problem to be well-posed in the distribution space.frFonctions à valeurs vectorielles, Distributions à valeurs vectorielles, Semi-groupe distributions, Problème de CauchyVector-valued functions, Vector-valued Distributions, Semi-group distributions, Cauchy problem.Thesis