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Decay estimates of solutions of a nonlinearly damped semilinear wave equation

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Guesmia A., Messaoudi S.

Annales Polonici Mathematici

2005

tom 85

nr 1

25-36

We consider an initial boundary value problem for the equation $u_{tt} - Δu - ∇ϕ·∇u + f(u) + g(u_{t}) = 0$. We first prove local and global existence results under suitable conditions on f and g. Then we show that weak solutions decay either algebraically or exponentially depending on the rate of growth of g. This result improves and includes earlier decay results established by the authors.

Blow-up of solutions for the Kirchhoff equation of q-Laplacian type with nonlinear dissipation

100%

Benaissa A., Messaoudi S.

Colloquium Mathematicum

2002

tom 94

nr 1

103-109

We establish the blow-up of solutions to the Kirchhoff equation of q-Laplacian type with a nonlinear dissipative term $(|u_{t}|^{l-2} u_{t})_{t} - M(||A^{1/2}u||²₂)Au + |u_{t}|^{β} u_{t} = |u|^{p} u$, x ∈ Ω, t > 0.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Colloquium Mathematicum

2 Messaoudi S.

1 Benaissa A.

1 Guesmia A.

1 2005

1 2002

Wyniki wyszukiwania

Decay estimates of solutions of a nonlinearly damped semilinear wave equation

Blow-up of solutions for the Kirchhoff equation of q-Laplacian type with nonlinear dissipation