Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping–source interaction

By Marcelo Moreira Cavalcanti, Valéria N. Domingos Cavalcanti, Irena Lasiecka. 2007

289 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2e3696c86fac3ff2ebb269035572849c6b994652

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Asymptotic Stability of the Wave Equation on Compact Manifolds and Locally Distributed Damping: A Sharp Result (2010, background): “We can find more interesting explicit decay rates in Cavalcanti et al. [ 7 ].”
A class of fourth order wave equations with dissipative and nonlinear strain terms (2008, background): “And there are only a few works on high order nonlinear evolution equations [3–31].”
On a wave equation with supercritical interior and boundary sources and damping terms (2011, background): “While energy decay has been extensively studied for interior sources up to the critical level (see for instance the overviews in [2], [3], [11], [16], [23], [30]), few results are available for boundary sources (still up to the critical order) [12], [14], [22], [28]; and none, to our knowledge, for ”
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.”
Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping (2008, background): “References [20] and [9] provide additionally an analysis of asymptotic decay rates to zero equilibrium of finite energy solutions.”
On existence, uniform decay rates and blow up for solutions of the 2-D wave equation with exponential source (2009, methodology): “For the reader’s convenience, we shall repeat (verbatim) the same arguments introduced firstly in Cavalcanti et al. [ 9 ].”