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The manuscript is subdivided into four chapters in addition to an introduction containing a fairlybrief presentation and bibliographical review of the work already undertaken on the topic ad-dressed. A plan of the manuscript is also inserted. In the first chapter, we present some necessaryconcepts related to the half-group theory, which we will use in the second and third chapters. Thesecond chapter deal with a coupled system of differential equations with nonlocal conditions. Wereduce the problem posed to an abstract first-order differential equation, whose coeficient near thederivative is a generally non-invertible operator. Using the results of chapter one, we establishexistence and uniqueness results for the reduced problem. Thus of the studied problem. In thethird chapter we study a boundary problem for parabolic equation with integral conditions. Sucha condition is not regular. The study method is based on the reduction of the posed problem to anequivalent problem for abstract differential equation with integral condition. Thus, the operatorinduced by the problem posed has a non-dense domain, and not self-adjoint.