Total variation flow perturbed by gradient linear multiplicative noise

Munteanu I, Röckner M (2018)
Infinite Dimensional Analysis, Quantum Probability and Related Topics 21(1): 1850003 .

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
We consider stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative gradient-type noise. We study existence and uniqueness of non-negative variational solutions in terms of stochastic variational inequalities. We also show the positivity preserving property of the solutions and extinction in finite time with probability one. These kinds of equations arise, e.g., in the use for simulation of image restoring techniques or for modeling turbulence.
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Infinite Dimensional Analysis, Quantum Probability and Related Topics
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21
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1
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1850003
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Munteanu I, Röckner M. Total variation flow perturbed by gradient linear multiplicative noise. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 2018;21(1): 1850003 .
Munteanu, I., & Röckner, M. (2018). Total variation flow perturbed by gradient linear multiplicative noise. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 21(1), 1850003 . doi:10.1142/S0219025718500030
Munteanu, I., and Röckner, M. (2018). Total variation flow perturbed by gradient linear multiplicative noise. Infinite Dimensional Analysis, Quantum Probability and Related Topics 21:1850003 .
Munteanu, I., & Röckner, M., 2018. Total variation flow perturbed by gradient linear multiplicative noise. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 21(1): 1850003 .
I. Munteanu and M. Röckner, “Total variation flow perturbed by gradient linear multiplicative noise”, Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 21, 2018, : 1850003 .
Munteanu, I., Röckner, M.: Total variation flow perturbed by gradient linear multiplicative noise. Infinite Dimensional Analysis, Quantum Probability and Related Topics. 21, : 1850003 (2018).
Munteanu, Ionut, and Röckner, Michael. “Total variation flow perturbed by gradient linear multiplicative noise”. Infinite Dimensional Analysis, Quantum Probability and Related Topics 21.1 (2018): 1850003 .