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Hamilton-Jacobi Equations

Show simple item record 2017-06-09T09:59:31Z und 2017-10-24T12:22:15Z 2017-06-09T09:59:31Z und 2017-10-24T12:22:15Z 2017-06-09T09:59:31Z
dc.identifier.uri und
dc.title Hamilton-Jacobi Equations en
ethesis.discipline Mathematics en
ethesis.discipline Matematiikka fi
ethesis.discipline Matematik sv
ethesis.department Institutionen för matematik och statistik sv
ethesis.department Department of Mathematics and Statistics en
ethesis.department Matematiikan ja tilastotieteen laitos fi
ethesis.faculty Matematisk-naturvetenskapliga fakulteten sv
ethesis.faculty Matemaattis-luonnontieteellinen tiedekunta fi
ethesis.faculty Faculty of Science en
ethesis.faculty.URI Helsingfors universitet sv University of Helsinki en Helsingin yliopisto fi
dct.creator Skourat, Nikita
dct.issued 2017
dct.language.ISO639-2 eng
dct.abstract This thesis presents the theory of Hamilton-Jacobi equations. It is first shown how the equation is derived from the Lagrangian mechanics, then the traditional methods for searching for the solution are presented, where the Hopf-Lax formula along with the appropriate notion of the weak solution is defined. Later the flaws of this approach are remarked and the new notion of viscosity solutions is introduced in connection with Hamilton-Jacobi equation. The important properties of the viscosity solution, such as consistency with the classical solution and the stability are proved. The introduction into the control theory is presented, in which the Hamilton-Jacobi-Bellman equation is introduced along with the existence theorem. Finally multiple numerical methods are introduced and aligned with the theory of viscosity solutions. The knowledge of the theory of partial differential analysis, calculus and real analysis will be helpful. en
dct.language en
ethesis.language English en
ethesis.language englanti fi
ethesis.language engelska sv
ethesis.thesistype pro gradu-avhandlingar sv
ethesis.thesistype pro gradu -tutkielmat fi
ethesis.thesistype master's thesis en
dct.identifier.urn URN:NBN:fi-fe2017112252370
dc.type.dcmitype Text

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