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Authors: MOSBAH KADDOUR, FARID MESSELMI.
Published Online: 2023-03-20
Published Print: 2023-04-30
pp. 213-234
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This work studies the initial boundary value problem for the Petrovsky equation with nonlinear damping................................ where Ω is open and bounded domain in Rn with a smooth boundary ∂Ω = Γ, α, and β > 0. For the nonlinear continuous term f (u) and for g continuous, increasing, satisfying g (0) = 0, under suitable conditions, the global existence of the solution is proved by using the Faedo-Galerkin argument combined with the stable set method in H2 (Ω). Furthermore, we show that this solution blows up in a finite time when the initial energy is negative.
Mathematics Subject Classification (2010): 93C20, 93D15.
Keywords: Global existence, blow-up, nonlinear source, nonlinear dissipative, Petrovsky equation
