Existence and Asymptotic Behavior for a Strongly Damped Nonlinear Wave Equation
1980 ◽
Vol 32
(3)
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pp. 631-643
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Keyword(s):
In this paper we study the nonlinear initial boundary value problem(1.1) ωtt— αΔ ωt— Δω= f(ω), t> 0ω(x, 0) = ϕ(x), x∈ Ωωt(x, 0) = ψ (x), x∈ Ωω(x, t ) = 0, x ∈ ∂Ω, t ≥ 0.In (1.1) Ω is a smooth bounded domain in Rn, n = 1, 2, 3, α > 0, and f ∈ C1(R;R) with f‘(x) ≦ co for all x ∈ R (where c0 is a nonnegative constant), lim sup|x|→+∞f(x)/x ≦0, and f(0) = 0. Our objective will be to establish the existence of unique strong global solutions to (1.1) and investigate their behavior as t→ +∞.Our approach takes advantage of the semilinear character of (1.1) and reformulates the problem as an abstract ordinary differential equation in a Banach space.
2007 ◽
Vol 147
(1)
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pp. 6470-6482
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2007 ◽
Vol 2007
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pp. 1-9
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2014 ◽
Vol 638-640
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pp. 1691-1694
2013 ◽
Vol 411-414
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pp. 1419-1422
2013 ◽
Vol 11
(02)
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pp. 1350017
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2008 ◽
Vol 18
(08)
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pp. 1383-1408
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1987 ◽
Vol 16
(4-6)
◽
pp. 735-761
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2013 ◽
Vol 2013
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pp. 1-7
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