Existence of global solutions to a quasilinear wave equation with general nonlinear damping
Electronic Journal of Differential Equations, 2002 In this paper we prove the existence of a global solution and study its decay for the solutions to a quasilinear wave equation with a general nonlinear dissipative term by constructing a stable set in $H^{2}cap H_{0}^{1}$.
Mohammed Aassila, Abbes Benaissa
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Exponential energy decay and blow-up of solutions for a system of nonlinear viscoelastic wave equations with strong damping [PDF]
Boundary Value Problems, 2011 In this paper, we consider the system of nonlinear viscoelastic equations u t t - Δ u + ∫ 0 t g 1 ( t - τ ) Δ u ( τ ) d τ - Δ u t = f 1 ( u , v ) , ( x , t )
Liang Fei, Gao Hongjun
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Advances in Difference Equations, 2011 A second-order abstract problem of neutral type with derivatives of non-integer order in the nonlinearity as well as in the nonlocal conditions is investigated. This model covers many of the existing models in the literature. It extends the integer order
Tatar Nasser-eddine
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Global nonexistence of solution for coupled nonlinear Klein-Gordon with degenerate damping and source terms [PDF]
, 2022 In this article we consider a coupled system of nonlinear Klein-Gordon equations with degenerate damping and source terms. We prove, with positive initial energy, the global nonexistence of solutions by concavity method.
KHALILI, Zineb +2 more
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Global nonexistence of solutions to system of Klein-Gordon equations with degenerate damping and strong source terms in viscoelasticity [PDF]
, 2022 In this paper, we consider a system of nonlinear viscoelastic wave equations with degenerate damping and source terms. We prove, with positive initial energy, the global nonexistence of solution by concavity method.
OUCHENANE, Djamel +2 more
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Global existence and stability of solution for a p−Kirchhoff type hyperbolic equation with damping and source terms [PDF]
, 2022 In this paper, we consider a nonlinear p−Kirchhoff type hyperbolic equation with damping and source terms f utt − M Ω |∇u|p dx ∆pu + |ut| m−2 ut = |u| r−2 u.
MAOUNI, Messaoud +2 more
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Decay rate of solutions to the Cauchy problem for a coupled system of a viscoelastic wave equations with a strong delay in Rⁿ [PDF]
, 2023 Using weighted spaces, we establish a general decay rate properties of solutions as T→∞ for a coupled system of a viscoelastic wave equations in Rn under some conditions on g1, g2, ϕ.
BELHADJI, Bochra +2 more
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Exponential decay of the viscoelastic wave equation of Kirchhoff type with a nonlocal dissipation [PDF]
, 2020 The following viscoelastic wave equation of Kirchhoff type with non- linear and nonlocal damping utt − ψ (I I2\ 2 ∆u − α∆ut t + g(t − τ )∆u(τ )dτ + M 0 (I∇uI2\ u = f (u), where M (r) is a C1([0, ∞)) -function satisfying M (r) ≥ m1 > 0 for r ≥ 0, is ...
MELLAH, Mohamed, HAKEM, Ali
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Abstract and Applied Analysis, Volume 2004, Issue 11, Page 935-955, 2004., 2004 We prove the global existence and study decay properties of the solutions to the wave equation with a weak nonlinear dissipative term by constructing a stable set in H1(ℝn).
Abbès Benaissa, Soufiane Mokeddem
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Blowup of solutions with positive energy in nonlinear thermoelasticity with second sound
Journal of Applied Mathematics, Volume 2004, Issue 3, Page 201-211, 2004., 2004 This work is concerned with a semilinear thermoelastic system, where the heat flux is given by Cattaneo′s law instead of the usual Fourier′s law. We will improve our earlier result by showing that the blowup can be obtained for solutions with “relatively” positive initial energy.
Salim A. Messaoudi, Belkacem Said-Houari
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