We discuss global existence and asymptotic behaviour of a price formation free boundary model introduced by Lasry and Lions in 2007. Our results are based on a construction which transforms the problem into the heat equation with specially prepared initial datum. The key point is that the free boundary present in the original problem becomes the zero level set of this solution. Using the properties of the heat operator we can show global existence, regularity and asymptotic results of the free boundary.
Nous discutons lʼexistence globale et le comportement local dʼun modèle de formation de prix introduit par Lasry et Lions en 2007. Nos résultats reposent sur une transformation reliant ce problème à une solution de lʼéquation de la chaleur avec données initiales particulières. Le point clé est que la frontière libre, présente dans le problème original, est conservée comme ensemble de niveau zéro de cette solution. Utilisant les propriétés de lʼopérateur de la chaleur nous pouvons montrer des résultats de régularité de la frontière libre et par suite lʼexistence globale.
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Luis A. Caffarelli 1; Peter A. Markowich 2, 3; Jan-F. Pietschmann 2
@article{CRMATH_2011__349_11-12_621_0, author = {Luis A. Caffarelli and Peter A. Markowich and Jan-F. Pietschmann}, title = {On a price formation free boundary model by {Lasry} and {Lions}}, journal = {Comptes Rendus. Math\'ematique}, pages = {621--624}, publisher = {Elsevier}, volume = {349}, number = {11-12}, year = {2011}, doi = {10.1016/j.crma.2011.05.011}, language = {en}, }
TY - JOUR AU - Luis A. Caffarelli AU - Peter A. Markowich AU - Jan-F. Pietschmann TI - On a price formation free boundary model by Lasry and Lions JO - Comptes Rendus. Mathématique PY - 2011 SP - 621 EP - 624 VL - 349 IS - 11-12 PB - Elsevier DO - 10.1016/j.crma.2011.05.011 LA - en ID - CRMATH_2011__349_11-12_621_0 ER -
Luis A. Caffarelli; Peter A. Markowich; Jan-F. Pietschmann. On a price formation free boundary model by Lasry and Lions. Comptes Rendus. Mathématique, Volume 349 (2011) no. 11-12, pp. 621-624. doi : 10.1016/j.crma.2011.05.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.05.011/
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