On nonlinear wave equations with degenerate damping and source terms

By Viorel Barbu, Irena Lasiecka, Mohammad Rammaha. 2005

91 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5532a1a0728e790eb8cfce7ae67b81b936a7f128

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping (2008, background): “This has been recognized in the literature first in the case of ⁀interior sources [15, 28, 32, 3] and, more recently, in the case of boundary sources [20, 31, 5].”
On a system of nonlinear wave equations with Balakrishnan–Taylor damping (2013, unknown): “The well-posedness is by now well established and can be found in the cited references (see also [5,20,24, 30]).”
Long-time dynamics of Kirchhoff wave models with strong nonlinear damping (2010, background): “We refer to [3, 11, 20, 24, 39, 40] for the case of a damping with a displacement-dependent coefficient and to [12, 13, 14] and to the references therein for a velocitydependent damping.”
Blow‐up of solutions for a viscoelastic wave equation with variable exponents (2019, background): “System (14)-(15) possesses a local solution in [0, tk), 0 < tk < T for an arbitrary T > 0.”
On existence, uniform decay rates and blow up for solutions of the 2-D wave equation with exponential source (2009, background): “See, for instance the followingworks: [1,5,7–12,14–16,18–20,25–32,34–36] and a long list of references therein.”
Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping (2008, background): “For supercritical interior sources, [13] and [3] exhibited existence, but no uniqueness, of weak solutions for a bounded domain Ω, under the restriction p < 6m/(m + 1), while in [36] the same results were obtained for Ω = R3, and compactly supported initial data, with p < 6m/(m + 1).”
On a wave equation with supercritical interior and boundary sources and damping terms (2011, background): “However, even without nonlinear boundary dynamics, an interior source of a super-critical order (3 < p ≤ 5) substantially perturbs the evolution generator so that the presence of damping becomes essential even for the local existence theory [6], [18], [32], [39]; the latter references along with [3]”