Mathématiques

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Study of a quasi-linear boundary problem with non-regular
(20 August 1955 university of Skikda, 2024-06-26) BOUNAAMA .Abir; MAOUNI .Messaoud
In this dissertation, we study some quasilinear hyperbolic equations with source terms in three parts. In the first part, we prove the global existence of solutions by using the potential and Nihari’s functional for a quasilinear hyperbolic problem involving the weighted Laplacian and p−Laplacian operator, after that, by using the Nakao’s inequality we study the decay of solutions and finally, we establish the blow up of solutions. In the second part, we prove the global existence results for a hyperbolic problem involving the fractional Laplacian operator and we study the blow up of solutions by using the concavity method. In the third part, we consider the boundary value problem related to the hyperbolic wave equation with non-regular boundary condition, we show the local existence theorem and we prove the finite time blow up resu