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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/220389
La teoria de DiPerna-Lions per a l’equació lineal del transport
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S’estudia l’esquema presentat per R.J. DiPerna i P.L. Lions l’any 1989 per a demostrar l’existència i la unicitat de solucions de l’equació lineal del transport amb camp de velocitats en un espai de Sobolev i de divergència fitada, així com un contraexemple a la unicitat que palesa que certes hipòtesis no poden ser relaxades. S’examina també com s’estén aquesta teoria a l’equació de Fokker-Planck, tot obtenint-ne resultats anàlegs al cas del transport.
We study the work presented by R.J. DiPerna and P.L. Lions in 1989 to prove the existence and uniqueness of solutions to the linear transport equation with velocity field in a Sobolev space and bounded divergence, as well as a counterexample showing that certain assumptions cannot be relaxed. We also explore how this theory extends to the Fokker-Planck equation, obtaining analogous results to those in the transport case.
We study the work presented by R.J. DiPerna and P.L. Lions in 1989 to prove the existence and uniqueness of solutions to the linear transport equation with velocity field in a Sobolev space and bounded divergence, as well as a counterexample showing that certain assumptions cannot be relaxed. We also explore how this theory extends to the Fokker-Planck equation, obtaining analogous results to those in the transport case.
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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2024, Director: Albert Clop
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RIU PONT, Jordi. La teoria de DiPerna-Lions per a l’equació lineal del transport. [consulted: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/220389