LEADER 04020nam 22005655 450 001 9910633918803321 005 20251113193927.0 010 $a981-19-6434-3 024 7 $a10.1007/978-981-19-6434-3 035 $a(MiAaPQ)EBC7151632 035 $a(Au-PeEL)EBL7151632 035 $a(CKB)25554171000041 035 $a(OCoLC)1356008553 035 $a(DE-He213)978-981-19-6434-3 035 $a(EXLCZ)9925554171000041 100 $a20221202d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aQualitative Properties of Dispersive PDEs /$fedited by Vladimir Georgiev, Alessandro Michelangeli, Raffaele Scandone 205 $a1st ed. 2022. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2022. 215 $a1 online resource (246 pages) 225 1 $aSpringer INdAM Series,$x2281-5198 ;$v52 311 08$aPrint version: Georgiev, Vladimir Qualitative Properties of Dispersive PDEs Singapore : Springer,c2023 9789811964336 320 $aIncludes bibliographical references and index. 327 $aPart I: Long-time behavior of NLS-type equations -- 1 Scipio Cuccagna, Note on small data soliton selection for nonlinear Schrödinger equations with potential -- 2 Jacopo Bellazzini and Luigi Forcella, Dynamics of solutions to the Gross-Pitaevskii equation describing dipolar Bose-Einstein condensates -- Part II: Probabilistic and nonstandard methods in the study of NLS equations -- 3 Renato Luca, Almost sure pointwise convergence of the cubic nonlinear Schrödinger equation on T^2 -- 4 Nevena Dugand?ija and Ivana Vojnovi?, Nonlinear Schrödinger equation with singularities -- Part III: Dispersive properties -- 5 Vladimir Georgiev, Alessandro Michelangeli, Raffaele Scandone, Schrödinger flow's dispersive estimates in a regime of re-scaled potentials -- 6 Federico Cacciafesta, Eric Sere, Junyong Zhang, Dispersive estimates for the Dirac-Coulomb equation -- 7 Matteo Gallone, Alessandro Michelangeli, Eugenio Pozzoli, Heat equation with inverse-square potential of bridging type across twohalf-lines -- Part IV: Wave and Kdv-type equations -- 8 Felice Iandoli, On the Cauchy problem for quasi-linear Hamiltonian KdV-type equations -- 9 Vladimir Georgiev and Sandra Lucente, Linear and nonlinear interaction for wave equations with time variable coefficients -- 10 Matteo Gallone and Antonio Ponno, Hamiltonian field theory close to the wave equation: from Fermi-Pasta-Ulam to water waves. 330 $aThis book provides a valuable collection of contributions by distinguished scholars presenting the state of the art and some of the most significant latest developments and future challenges in the field of dispersive partial differential equations. The material covers four major lines: (1) Long time behaviour of NLS-type equations, (2) probabilistic and nonstandard methods in the study of NLS equation, (3) dispersive properties for heat-, Schrödinger-, and Dirac-type flows, (4) wave and KdV-type equations. Across a variety of applications an amount of crucial mathematical tools are discussed, whose applicability and versatility goes beyond the specific models presented here. Furthermore, all contributions include updated and comparative literature. 410 0$aSpringer INdAM Series,$x2281-5198 ;$v52 606 $aDifferential equations 606 $aFunctional analysis 606 $aDifferential Equations 606 $aFunctional Analysis 615 0$aDifferential equations. 615 0$aFunctional analysis. 615 14$aDifferential Equations. 615 24$aFunctional Analysis. 676 $a515.35 702 $aMichelangeli$b Alessandro 702 $aScandone$b Raffaele 702 $aGeorgiev$b Vladimir 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910633918803321 996 $aQualitative properties of dispersive PDEs$93084141 997 $aUNINA