Study of a quasi-linear boundary problem with non-regular
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Date
2024-06-26
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20 August 1955 university of Skikda
Abstract
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
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Keywords
boundary problem, quasi-linear