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

","angewandte-chemie":"I. Munteanu, and M. Röckner, “Total variation flow perturbed by gradient linear multiplicative noise”, Total variation flow perturbed by gradient linear multiplicative noise.

Infinite Dimensional Analysis, Quantum Probability and Related Topics 21(1): 1850003 .","apa":"Munteanu, I., & Röckner, M. (2018). Total variation flow perturbed by gradient linear multiplicative noise.

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 . World Scientific . doi:10.1142/S0219025718500030.

","harvard1":"Munteanu, I., & Röckner, M., 2018. Total variation flow perturbed by gradient linear multiplicative noise. Munteanu, Ionut, and Röckner, Michael. 2018. “Total variation flow perturbed by gradient linear multiplicative noise”. *Infinite Dimensional Analysis, Quantum Probability and Related Topics* 21 (1): 1850003 .

"},"user_id":"89573","doi":"10.1142/S0219025718500030","year":"2018","author":[{"full_name":"Munteanu, Ionut","last_name":"Munteanu","first_name":"Ionut"},{"id":"10585","last_name":"Röckner","first_name":"Michael","full_name":"Röckner, Michael"}],"issue":"1","keyword":["Stochastic variational inequality","singular diffusivity","total variation","flow","multiplicative gradient-type Stratonovich noise"],"type":"journal_article","publication_identifier":{"issn":["0219-0257"],"eissn":["1793-6306"]},"isi":1,"external_id":{"isi":["000428372800003"]},"article_type":"original","date_created":"2018-04-23T07:44:40Z","publication_status":"published","article_number":"1850003 ","abstract":[{"lang":"eng","text":"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."}],"intvolume":" 21"}]