Rothe time-discretization method applied to a quasilinear wave equation subject to integral conditions.
Bouziani, Abdelfatah, Merazga, Nabil (2004)
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Bouziani, Abdelfatah, Merazga, Nabil (2004)
Advances in Difference Equations [electronic only]
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El Hachimi, Abderrahmane, Ammi, Moulay Rachid Sidi (2005)
International Journal of Mathematics and Mathematical Sciences
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Qi Tang, Kewei Zhang (2007)
Annales de l'I.H.P. Analyse non linéaire
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Merazga, Nabil, Bouziani, Abdelfatah (2005)
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Andrzej Rozkosz (2013)
Open Mathematics
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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.