1985
DOI: 10.1016/0022-0396(85)90008-7
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Nonlinear second order equations with applications to partial differential equations

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Cited by 39 publications
(27 citation statements)
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“…This quasimonotonicity assumption has been finally removed (even in a more general unbounded domain setting) in [50] using the combination of the above smoothing property with the technique of [62]. The closest to our study are the results and methods of [50] where the regularity of the global attractor in the energy phase space for three-dimensional problem (1.6) with non-linear term growing as u|u| 4 is established, see also [49] and [56].…”
Section: Introductionmentioning
confidence: 90%
“…This quasimonotonicity assumption has been finally removed (even in a more general unbounded domain setting) in [50] using the combination of the above smoothing property with the technique of [62]. The closest to our study are the results and methods of [50] where the regularity of the global attractor in the energy phase space for three-dimensional problem (1.6) with non-linear term growing as u|u| 4 is established, see also [49] and [56].…”
Section: Introductionmentioning
confidence: 90%
“…This gave rise to the question of the convergence of solutions when p tends to zero. Under a supplementary hypothesis on the nonlinear terms G (still satisfied by G's in the examples) (6) (G(w), « Strong » means that each term in (1) is a continuous H-valued function of t. The existence and uniqueness of such solutions is proved in [1], Our proof combines intégral équation approach from [1], factorization of second order (in time) équations and higher order energy estimâtes similar to (3), (4), (5).…”
Section: Moreover a Vector In H Y H With Exactly One Nonzero Componementioning
confidence: 99%
“…This leads to the following equations: (1) Xi,n+i(A"(A -A) -A"-1^-Bn) = I, Xhk = Xn+1~kXhn+i for 1 < k < n. From (6) we obtain…”
Section: Proof (I) -> (Ii) Let a G P(a) Then There Are Bounded Opementioning
confidence: 99%