Browsing by Author "Khaldi ,Aya"

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    Study of the existence and uniqueness,stability, regularityof the solution of certain classes of parabolic and hyperbolic PDEs
    (université 20aout 55 skikda, 2023) Khaldi ,Aya; Messaoud, MAOUNI
    The aim of this thesis is the study of global existence and asymptotic behavior of solutions for three types of systems with variable exponents. In the first type, we consider a nonlinear Kirchhoff type reaction diffusion equations with variable exponents and source terms, we prove with suitable assumptions on the variable exponents the global existence of the solution and stability result with positive initial energy. In the second type, we consider a nonlinear hyperbolic equation with multiple (x) Laplacian and variable exponent nonlinearities, we prove with negative initial energy the blow up of solutions. In the third type, we study fractional p-Kirchhoff type hyperbolic equations with damping and source terms. We also prove the existence of weak solution, and the stability results with negative initial energy. The proofs of the existence of global solutions are based on Faedo-Galerkin approximation combined with the potential and Nihari’s functional. Furthermore, the stability results being based on Komornik’s inequality