00651nas a2200157 4500008004100000245009600041210006900137260005800206300001400264490000600278100001700284700001700301700002200318700002400340856012900364 2016 eng d00aShip Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model0 aShip Sinkage and Trim Predictions Based on a CAD Interfaced Full bInternational Society of Offshore and Polar Engineers a511–5180 v31 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/ship-sinkage-and-trim-predictions-based-cad-interfaced-fully-nonlinear-potential-model01296nas a2200145 4500008004100000022001300041245010400054210006900158300001400227490000700241520073600248100002400984700002001008856012201028 2012 eng d a0951771500aSobolev quasi-periodic solutions of multidimensional wave equations with a multiplicative potential0 aSobolev quasiperiodic solutions of multidimensional wave equatio a2579-26130 v253 aWe prove the existence of quasi-periodic solutions for wave equations with a multiplicative potential on T d , d ≥ 1, and finitely differentiable nonlinearities, quasi-periodically forced in time. The only external parameter is the length of the frequency vector. The solutions have Sobolev regularity both in time and space. The proof is based on a Nash-Moser iterative scheme as in [5]. The key tame estimates for the inverse linearized operators are obtained by a multiscale inductive argument, which is more difficult than for NLS due to the dispersion relation of the wave equation. We prove the 'separation properties' of the small divisors assuming weaker non-resonance conditions than in [11]. © 2012 IOP Publishing Ltd.1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/sobolev-quasi-periodic-solutions-multidimensional-wave-equations-multiplicative01245nas a2200145 4500008004100000022001300041245008800054210006900142300001200211490000800223520070400231100002400935700002000959856012000979 2010 eng d a0003952700aSobolev periodic solutions of nonlinear wave equations in higher spatial dimensions0 aSobolev periodic solutions of nonlinear wave equations in higher a609-6420 v1953 aWe prove the existence of Cantor families of periodic solutions for nonlinear wave equations in higher spatial dimensions with periodic boundary conditions. We study both forced and autonomous PDEs. In the latter case our theorems generalize previous results of Bourgain to more general nonlinearities of class C k and assuming weaker non-resonance conditions. Our solutions have Sobolev regularity both in time and space. The proofs are based on a differentiable Nash-Moser iteration scheme, where it is sufficient to get estimates of interpolation-type for the inverse linearized operators. Our approach works also in presence of very large "clusters of small divisors". © Springer-Verlag (2009).1 aBerti, Massimiliano1 aBolle, Philippe uhttps://www.math.sissa.it/publication/sobolev-periodic-solutions-nonlinear-wave-equations-higher-spatial-dimensions00322nas a2200097 4500008004100000245004600041210004600087260003100133100002400164856003600188 2004 en d00aSoluzioni periodiche di PDEs Hamiltoniane0 aSoluzioni periodiche di PDEs Hamiltoniane bUnione Matematica Italiana1 aBerti, Massimiliano uhttp://hdl.handle.net/1963/4582