Abstract
In this paper we study well-posedness of the damped nonlinear wave equation in Ω × (0, ∞) with initial and Dirichlet boundary condition, where Ω is a bounded domain in ℝ2; ω⩾0, ωλ1+µ>0 with λ1 being the first eigenvalue of −Δ under zero boundary condition. Under the assumptions that g(·) is a function with exponential growth at the infinity and the initial data lie in some suitable sets we establish several results concerning local existence, global existence, uniqueness and finite time blow-up property and uniform decay estimates of the energy. Copyright © 2010 John Wiley & Sons, Ltd.
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