工学部_研究紹介_2020_英語版

71/80

Mamoru OkamotoNonlinear Partial Differential EquationsManyphysical,chemical,andbiologicalphenomenacanbemodeledusingdifferentialequations,whichareinmanycasesnonlinear.But,itisdifficulttofindasolutionoftheCauchyproblem(initialvalueproblem)fornonlinearpartialdifferentialequations(PDEs)becauseofitsnonlinearity.Well-posednessoftheCauchyproblemthereforeisimportantandafirststepofstudyfornonlinearPDEs.Here,well-posednessmeansthattheexistenceofasolution,uniqueness,andcontinuousdependenceofinitialdata.Assistant ProfessorHe received doctor's degree of science from Kyoto University.His research interest is nonlinear partial differential equations.Ouraimistoobtainlowregularitywell-posednessoftheCauchyproblemfornonlinearpartialdifferentialequations(PDEs),especiallynonlineardispersiveandwaveequations.Ifnonlinearpartshavesymmetry,namelyisinvariantundersometransformations,onecanexpectthattheworstinteractioniscancelledout.ConstructionofatheoryforthesecancellationpropertiesisourgoalandthatwillcontributetheevolutionofawiderangeofnonlinearPDEs.Inordertomoreadvancedresearch,somegraduatedstudentsofourlaboratoryenteragraduateschool.Otherstudentsfindajobincompanies.In seminars, besides understanding mathematical statements, good presentation skills are also required.In the FutureAfter GraduationEngineering Core AkitoSuzukiMycurrentresearchinterestfocusesonthespectraofelectronsinhydrogenatedgraphenes.Grapheneisananomaterialcomposedofcarbonatomsthatarearrangedinatwodimensionalhoneycomblattice.Whilegrapheneisasemiconductorwithzerobandgap,fullyhydrogenatedgraphene,whichisinparticularcalledgraphane(withana),isaninsulatorwithabandgap.Iaminterestedinthespectraofelectronsinpartiallyhydrogenatedgraphenes.AssociateProfessorResearchInterests:MathematicalPhysics,SpectralAnalysisKeywords:QuantumFieldTheory,DiscreteLaplacianMathematical Physics :Mathematics sheds light on physical phenomenaThestructureofsuchamaterialismathematicallydescribedbyagraphthatiscomposedofthesetofverticesandedges.Atomsinthematerialaredescribedbytheverticesandatomicbondsbytheedges.ThentheLaplaceoperatoronthegraphbecomestheHamiltonianofanelectronmovinginthematerial.ThespectrumofthisHamiltoniancorrespondstotheenergyoftheelectron.Thephysicalpropertieslikeelectricalconductivityareanalyzedviaspectralanalysisbymathematicssuchasfunctionalanalysis,operatortheoryandgraphtheory.Tostudythespectraofelectronsisanimportantprobleminmathematicalphysics.Engineering Core 69