Global existence and nonexistence for nonlinear wave equations with damping and source terms

Rammaha, Mohammad A.; Strei, Theresa A.

doi:10.1090/s0002-9947-02-03034-9

Cited by 68 publications

(10 citation statements)

References 24 publications

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“…2, 5, 7, and 22). However, when both damping and source are present, the analysis of their interaction and their influence on the global behavior of solutions becomes more difficult and has served as a motivation for this study (see also other related results 8,17,26,31,34,35 and the references therein).…”

Section: B Literature Overview and New Contributionsmentioning

confidence: 99%

Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources

Pei

Rammaha

Toundykov

2015

Journal of Mathematical Physics

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Articles you may be interested inBlow up of a solution for a system of nonlinear higher-orderwave equations with strong damping terms AIP Conf.Discrete rotating waves in a ring of coupled mechanical oscillators with strong damping Uniqueness of solutions to the helically reduced wave equation with Sommerfeld boundary conditionsThis paper investigates a quasilinear wave equation with Kelvin-Voigt damping,, in a bounded domain Ω ⊂ R 3 and subject to Dirichlét boundary conditions. The operator ∆ p , 2 < p < 3, denotes the classical p-Laplacian. The nonlinear term f (u) is a source feedback that is allowed to have a supercritical exponent, in the sense that the associated Nemytskii operator is not locally Lipschitz from W 1, p 0 (Ω) into L 2 (Ω). Under suitable assumptions on the parameters, we prove existence of local weak solutions, which can be extended globally provided the damping term dominates the source in an appropriate sense. Moreover, a blow-up result is proved for solutions with negative initial total energy. C 2015 AIP Publishing LLC.

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Section: B Literature Overview and New Contributionsmentioning

confidence: 99%

Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources

Pei

Rammaha

Toundykov

2015

Journal of Mathematical Physics

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“…We finish the literature overview by mentioning that there exists a huge literature regarding hyperbolic equations which involves degenerate source and damping terms. Here, we cite, for example . The majority of these papers deal with existence, nonexistence and blow‐up of solutions in finite time.…”

Section: Introductionmentioning

confidence: 99%

Unilateral problems for the wave equation with degenerate and localized nonlinear damping: well‐posedness and non‐stability results

Cavalcanti

Fatori

et al. 2018

Mathematische Nachrichten

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Unilateral problems related to the wave model subject to degenerate and localized nonlinear damping on a compact Riemannian manifold are considered. Our results are new and concern two main issues: (a) to prove the global well‐posedness of the variational problem; (b) to establish that the corresponding energy functional is not (uniformly) stable to equilibrium in general, namely, the energy does not converge to zero on the trajectory of every solution, even if a full linear damping is taken in place.

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“…Authors in Refs. studied that damping term can lead to the solutions of problems blasting in a limited time for the linear hyperbolic problems. Authors in Refs.…”

Section: Introductionmentioning

confidence: 99%

A penalty‐FEM for navier‐stokes type variational inequality with nonlinear damping term

Qiu

Mei

Xue

2017

Numerical Methods Partial

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In this article, we consider a penalty finite element (FE) method for incompressible Navier‐Stokes type variational inequality with nonlinear damping term. First, we establish penalty variational formulation and prove the well‐posedness and convergence of this problem. Then we show the penalty FE scheme and derive some error estimates. Finally, we give some numerical results to verify the theoretical rate of convergence. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 918–940, 2017

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Global existence and nonexistence for nonlinear wave equations with damping and source terms

Cited by 68 publications

References 24 publications

Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources

Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources

Unilateral problems for the wave equation with degenerate and localized nonlinear damping: well‐posedness and non‐stability results

A penalty‐FEM for navier‐stokes type variational inequality with nonlinear damping term

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