A game theoretical approximation for a parabolic/elliptic system with different operators | Zendy

Alfredo Miranda | Zendy; Julio D. Rossi | Zendy

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A game theoretical approximation for a parabolic/elliptic system with different operators

Author(s) -

Alfredo Miranda,

Julio D. Rossi

Publication year - 2022

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2022034

Subject(s) - infinity , viscosity solution , mathematics , viscosity , laplace operator , value (mathematics) , zero (linguistics) , mathematical analysis , elliptic curve , parabolic partial differential equation , pure mathematics , partial differential equation , physics , linguistics , statistics , philosophy , quantum mechanics

In this paper we find viscosity solutions to a coupled system composed by two equations, the first one is parabolic and driven by the infinity Laplacian while the second one is elliptic and involves the usual Laplacian. We prove that there is a two-player zero-sum game played in two different boards with different rules in each board (in the first one we play a Tug-of-War game taking the number of plays into consideration and in the second board we move at random) whose value functions converge uniformly to a viscosity solution to the PDE system.

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