KIBECHE, Koudir2024-06-272024-06-272024https://dspace.univ-annaba.dz//handle/123456789/3545This thesis is devoted to the stud of the existence, the uniquenes sand the ymptotic behavior of some hyperbolictype problems,inthe first problem,,westudy then existence and the exponential stability of the solution of aporouselastic system with micro temperatures and adistributed internaldelayterm,the proof which we have established the exponential stability is based on the construction an appropriate Lyapunov function equivalent to the energy of the solution considered . This function checks fo radi¤erentialin equation leading to the result of the desireddecayPDFenporous system; mecrotemperature; exponential stability; wave equation; varying delay term; exponential stability; semigroup theory; lyapunov func- tional; delay terms in the feedbacks; distributed delay; viscoelastic; thermoelastic,; decay rateThesis