EXISTENCE AND DECAY RATE ESTIMATES FOR THE WAVE EQUATION WITH NONLINEAR BOUNDARY DAMPING AND SOURCE TERM

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Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions (2008, methodology): “Consequently, the same result can be established by using the Faedo-Galerkin approximation method coupled with the potential well method [7].”
Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping–source interaction (2007, background): “The case of sole interior source f (s)= |s|k−1k with subcritical exponent k < n n−2 , h = 0 and nonlinear boundary damping g(s) was treated in [7].”
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): “a polynomial structure, was established in earlier literature ([39, 36, 13, 3, 9] and references therein).”
Existence and asymptotic stability of a viscoelastic wave equation with a delay (2011, background): “We mention also the paper [ 7 ], in which the authors investigated a problem similar to (6) with a nonlinear feedback acting on the boundary of the domain Ω and showed uniform decay rates of the energy without imposing any restrictive growth assumption on the damping term.”