Compact attractor for a nonlinear wave equation with critical exponent
1990 ◽
Vol 115
(1-2)
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pp. 61-64
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SynopsisIn this paper we study the existence of a compact attractor for the solutions of the equation utt − Δu + cut + f(u) = h(t, x), x ∊ ℝ3. The phase space is H1 × L2 and periodicity in the x-variables is taken as a boundary condition. Besides the usual coercive condition, we assume f satisfies the growth condition |f′(u)|≦ a + bu2; this growth condition is critical because the embedding H1 → L6 is not compact. In the proof we use an Lp − H1.q estimate for the linear homogeneous wave equation.
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2002 ◽
Vol 44
(1)
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pp. 1-23
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2021 ◽
2020 ◽
Vol 13
(4)
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pp. 425-436
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2020 ◽
Vol 20
(4)
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pp. 444-456
2018 ◽
Vol 58
(9)
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pp. 1531-1543
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