Nonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noise

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

  • Ioana Ciotir
  • Jonas Tölle

Organisaatiot

  • Institut National des Sciences Appliquées de Rouen Normandie

Kuvaus

We study existence and uniqueness of a variational solution in terms of stochastic variational inequalities (SVI) to stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative Stratonovich gradient-type noise. We derive a commutator relation for the unbounded noise coefficients in terms of a geometric Killing vector condition. The drift term is given by the total variation flow, respectively, by a singular p-Laplace-type operator. We impose nonlinear zero Neumann boundary conditions and precisely investigate their connection with the coefficient fields of the noise. This solves an open problem posed in Barbu et al. (2013) [7] and Barbu and Röckner (2015) [10].

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut1764–1792
Sivumäärä29
JulkaisuJournal of Functional Analysis
Vuosikerta271
Numero7
TilaJulkaistu - lokakuuta 2016
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 4440147