Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise

Barbu V, Röckner M (2013)
Archive For Rational Mechanics And Analysis 209(3): 797-834.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Barbu, Viorel; Röckner, MichaelUniBi
Abstract / Bemerkung
In this work, we introduce a new method to prove the existence and uniqueness of a variational solution to the stochastic nonlinear diffusion equation where is a bounded and open domain in and W(t) is a Wiener process of the form and are independent Brownian motions. This is a stochastic diffusion equation with a highly singular diffusivity term. One main result established here is that for all initial conditions in , it is well posed in a class of continuous solutions to the corresponding stochastic variational inequality. Thus, one obtains a stochastic version of the (minimal) total variation flow. The new approach developed here also allows us to prove the finite time extinction of solutions in dimensions , which is another main result of this work.
Erscheinungsjahr
2013
Zeitschriftentitel
Archive For Rational Mechanics And Analysis
Band
209
Ausgabe
3
Seite(n)
797-834
ISSN
0003-9527
Page URI
https://pub.uni-bielefeld.de/record/2612709

Zitieren

Barbu V, Röckner M. Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise. Archive For Rational Mechanics And Analysis. 2013;209(3):797-834.
Barbu, V., & Röckner, M. (2013). Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise. Archive For Rational Mechanics And Analysis, 209(3), 797-834. doi:10.1007/s00205-013-0632-x
Barbu, V., and Röckner, M. (2013). Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise. Archive For Rational Mechanics And Analysis 209, 797-834.
Barbu, V., & Röckner, M., 2013. Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise. Archive For Rational Mechanics And Analysis, 209(3), p 797-834.
V. Barbu and M. Röckner, “Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise”, Archive For Rational Mechanics And Analysis, vol. 209, 2013, pp. 797-834.
Barbu, V., Röckner, M.: Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise. Archive For Rational Mechanics And Analysis. 209, 797-834 (2013).
Barbu, Viorel, and Röckner, Michael. “Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise”. Archive For Rational Mechanics And Analysis 209.3 (2013): 797-834.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar