Recent advances in pure and applied mathematics

186 Pages·2020·3.352 MB·English

by  Ortegon Gallego F., Garcia Garcia J.I (ed.)

RSME Springer Series 4
Francisco Ortegón Gallego
Juan Ignacio García García
Editors
Recent Advances
in Pure and Applied
Mathematics
RSME Springer Series
Volume 4
Editor-in-Chief
JoséBonet,UniversitatPolitècnicadeValència,InstitutoUniversitariodeMatemática
PurayAplicada(IUMPA),Valencia,Spain
SeriesEditors
Nicolas Andruskiewitsch, FaMAF - CIEM (CONICET) Universidad Nacional de
Córdoba,Córdoba,Argentina
MaríaEmiliaCaballero,InstitutodeMatemáticas,UniversidadNacionalAutónoma
deMéxico,México,México
Pablo Mira, Departamento de Matematica Aplicada y Estadistica, Universidad
PolitécnicadeCartagena,Cartagena,Spain
TimothyG.Myers,CentredeRecercaMatemàtica,Barcelona,Spain
MartaSanz-Solé,DepartmentofMathematicsandInformatics,BarcelonaGraduate
SchoolofMathematics(BGSMath),UniversitatdeBarcelona,Barcelona,Spain
Karl Schwede, Department of Mathematics, University of Utah, Salt Lake City,
USA
Asof2015,RSME-RealSociedadMatemáticaEspañola-andSpringercooperate
in order to publish works by authors and volume editors under the auspices of
a co-branded series of publications including advanced textbooks, Lecture Notes,
collectionsofsurveysresultingfrominternationalworkshopsandSummerSchools,
SpringerBriefs, monographs as well as contributed volumes and conference pro-
ceedings.Theworksin theseriesarewritteninEnglishonly,aimingtoofferhigh
level research results in the fields of pure and applied mathematics to a global
readershipofstudents,researchers,professionals,andpolicymakers.
Moreinformationaboutthisseriesathttp://www.springer.com/series/13759
Francisco Ortegón Gallego (cid:129)
Juan Ignacio García García
Editors
Recent Advances in Pure
and Applied Mathematics
Editors
FranciscoOrtegónGallego JuanIgnacioGarcíaGarcía
DepartmentofMathematics,Faculty DepartmentofMathematics,Faculty
ofMarineandEnvironmentalSciences ofSciences
UniversidaddeCádiz UniversidaddeCádiz
PuertoReal,Spain PuertoReal,Spain
ISSN2509-8888 ISSN2509-8896 (electronic)
RSMESpringerSeries
ISBN978-3-030-41320-0 ISBN978-3-030-41321-7 (eBook)
https://doi.org/10.1007/978-3-030-41321-7
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Preface
This volume is the result of academic and scientific collaboration between the
mathematicalcommunitiesfromSpainandBrazil.
In December 2015 the Federal University of Ceará (Brazil) organizedthe first
meetingbetweentheBrazilianMathematicalSociety(SBM),theBrazilianSociety
of Applied and Computational Mathematics (SBMAC), and the Real Sociedad
MatemáticaEspañola(RSME).Asaconsequenceofthesuccessofthatfirstedition,
the respective national societies decided to host a second meeting in Spain. The
University of Cádiz was chosen to organize the Second Meeting of the Brazilian
and Spanish mathematical societies, which took place from December 11 to 14,
2018.Moreover,inthissecondedition,theSpanishSocietyofAppliedMathematics
(SEMA)alsoparticipatedintheorganizationoftheevent.
Of course, the main objective of this second meeting was to continue to
strengthen the collaboration between researchers and institutions from Spain and
Brazil.Tothisend,plenaryconferences,specialsessions,andposterswereincluded
on a wide range of topics in Pure and Applied Mathematics. All of them were
submittedtothedemandsofaScientificCommitteeofthehighestlevel,comprising
chosenrepresentativesofthefourparticipatingsocieties.
Themeetingtookplaceinthe“Constitutionof1812”buildingandintheFaculty
of Philosophy and Letters of the University of Cádiz, both historical buildings in
theancientcityofCádiz.ItisworthmentioningthatCádizwaschosenasthevenue
forthismeetingasitisconsideredbyalltobeahistoricalcity,withgreatlinksto
theothersideoftheAtlanticandwithauniversitythathasinnumerablelinkswith
institutionsontheAmericancontinent.
TheBayofCádiz,whosebeautycouldbeappreciatedbyallparticipantsfromthe
congressvenue,hasbeenaplaceofreferenceforcountlessshipsandcruises.From
here,tradeandmaritimetransportwaspracticedwiththeWestandEastIndies,the
shoresoftheMediterraneanSea,thegreatAtlanticportsofEurope,andthecoasts
ofAfrica.Cádizhasbeenacosmopolitancitysincetheseventeenthcentury.
Building upon the success of this second meeting, we launch this volume in
whichavariedselectionofworkspresentedatthemeetinghavebeenincludedandin
whichqualityisthepredominantnote.Thelinesoftheselectedworksrangefrom
v
vi Preface
abstract algebra, such as Lie algebras, commutative semi-groups, and differential
geometry, to more applied works in which mathematical modeling by means of
boundaryvalueproblemsgovernedbyPDEsisthesubjectofstudy.Alltheworks
inthevolumehavebeensubmittedtoablindpeerreviewprocess.Inaddition,this
collectionoffersagoodsummaryoftherecentactivityofthedifferentSpanishand
Brazilian research groups interested in both the applications of mathematics and
puremathematics.
We would like to conclude this introductionby thanking all those who, in one
way oranother,participatedin theorganizationof thecongressand especiallythe
local organizingcommittee along with all the volunteers. Not only did they make
thecongresspossiblebutthepublicationofthisvolumeislargelytheresultoftheir
work. Finally, we would like to thank the authors themselves for submitting their
valuableworks.
PuertoReal,Spain JuanIgnacioGarcíaGarcía
PuertoReal,Spain FranciscoOrtegónGallego
December15,2019
Contents
OntheControloftheNavier-StokesEquationsandRelatedSystems ..... 1
EnriqueFernández-Cara
AsymptoticStabilityinSomeGenericClassesofThree-Dimensional
DiscontinuousDynamicalSystems............................................. 21
MarcoA.TeixeiraandDurvalJ.Tonon
RegularisationinEjection-CollisionOrbitsoftheRTBP ................... 35
MercèOllé,ÓscarRodríguez,andJaumeSoler
OnLocalAlgebrasofMaximalAlgebrasofJordanQuotients ............. 49
F.MontanerandI.Paniello
OntheNumericalBehaviorofaChemotaxisModelwithLinear
ProductionTerm ................................................................. 61
F.Guillén-González,M.A.Rodríguez-Bellido,andD.A.Rueda-Gómez
TheThin-SandwichProbleminGeneralRelativity.......................... 75
RodrigoAvalos
ParametricSolutionstoaStaticFourth-OrderEuler–Bernoulli
BeamEquationinTermsofLaméFunctions................................. 93
A.Ruiz,C.Muriel,andJ.Ramírez
OnLargeOrbitsofActionsofFiniteSolubleGroups:Applications....... 105
A.Ballester-Bolinches,R.Esteban-Romero,andH.Meng
PoissonAlgebrasandGraphs................................................... 115
AntonioJ.CalderónMartín,BoubacarDieme,andFranciscoJ.Navarro
Izquierdo
GraphswithWeightofFoldGaussMaps ..................................... 127
C.MendesdeJesusandE.Sanabria-Codesal
ANoteonSpacelikeHypersurfacesandTimelikeConformalVectors..... 135
GiulioColombo,JoséA.S.Pelegrín,andMarcoRigoli
vii
viii Contents
NaturallyGradedQuasi-FiliformAssociativeAlgebras..................... 149
I.A.KarimjanovandM.Ladra
SpacelikeHypersurfacesinConformallyStationarySpacetimes........... 161
LuisJ.Alías,AntonioCaminha,andF.YureS.doNascimento
Geodesic Completeness and the Quasi-Einstein Equation
forLocallyHomogeneousAffineSurfaces .................................... 175
P.B.GilkeyandX.Valle-Regueiro
On the Control of the Navier-Stokes
Equations and Related Systems
EnriqueFernández-Cara
Abstract Thiscontributionrelies on two main concepts:the Navier-Stokes equa-
tionsandcontroltheory.Ouraimistojustifytheirrelevanceand,also,todescribe
some results that can be obtained by working simultaneously with both them. In
particular,wewillrecallsomerecentresultsconcerningrelatedbi-objectiveoptimal
controlandcontrollabilityproblems.
1 Introduction
1.1 TheNavier-Stokes Equations
TheNavier-Stokesequationsdescribethebehaviorofanincompressiblefluidunder
realisticconditions.Thus,theycanbeusedtomodelalotofatmospheric,oceanic,
andclimatologicalphenomena,theflowofafluidaroundabodyofanykind,flows
inchannelsandassociatedjets,etc.Seeforinstance[3,67,79]forsomedetails.
Initssimplestform,theequationsarethefollowing:
⎧
(cid:6) (cid:7)
⎪⎪⎪⎪⎪⎪⎪⎨∂tu1−ν(cid:6)∂12u1+∂22u1+∂32u1(cid:7)+u1∂1u1+u2∂2u1+u3∂3u1+ρ11∂1p =f1
∂ u −ν ∂2u +∂2u +∂2u +u ∂ u +u ∂ u +u ∂ u + ∂ p =f
t 2 1 2 2 2 3 2 1 1 2 2 2 2 3 3 2 ρ 2 2
⎪⎪⎪⎪⎪⎪⎪⎩∂tu3−ν(cid:6)∂12u3+∂22u3+∂32u3(cid:7)+u1∂1u3+u2∂2u3+u3∂3u3+ρ1∂3p =f3
∂ u +∂ u +∂ u =0.
1 1 2 2 3 3
E.Fernández-Cara((cid:2))
Dpto.EDANandIMUS,UniversityofSevilla,Sevilla,Spain
e-mail:[email protected]
©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicence 1
toSpringerNatureSwitzerlandAG2020
F.OrtegónGallego,J.I.GarcíaGarcía(eds.),RecentAdvancesinPureandApplied
Mathematics,RSMESpringerSeries4,
https://doi.org/10.1007/978-3-030-41321-7_1