On mild solutions of gradient systems in Hilbert spaces

• Autorzy: Andrzej Rozkosz
• Języki publikacji: EN

Abstrakty

EN

We consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.

Słowa kluczowe

EN

Gradient systems; Ornstein-Uhlenbeck operator; Mild solution; Backward stochastic differential equation

Kategorie tematyczne

• 35R15: Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables)
• 60H30: Applications of stochastic analysis (to PDE, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 11
• Strony: 1994-2004

Daty

wydano

2013-11-01

online

2013-08-23

Twórcy

autor

Andrzej Rozkosz

• Nicolaus Copernicus University

Bibliografia

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• [7] Da Prato G., Zabczyk J., Second Order Partial Differential Equations in Hilbert Spaces, London Math. Soc. Lecture Note Ser., 293, Cambridge University Press, Cambridge, 2002 http://dx.doi.org/10.1017/CBO9780511543210
• [8] Fuhrman M., Tessitore G., Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control, Ann. Probab., 2002, 30(3), 1397–1465 http://dx.doi.org/10.1214/aop/1029867132
• [9] Oharu S., Takahashi T., Characterization of nonlinear semigroups associated with semilinear evolution equations, Trans. Amer. Math. Soc., 1989, 311(2), 593–619 http://dx.doi.org/10.1090/S0002-9947-1989-0978369-9

Identyfikatory

DOI

10.2478/s11533-013-0304-y