Self-repelling diffusions via an infinite dimensional approach

In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. Then we study the corresponding transition semigroup and, more precisely, we prove that it has Feller property and we give an explicit form of an invariant probability of the system.Comment: Version 2: Typos are corrected. Section 6 is reorganised in order to make it more transparent; the results are unchanged. The presentation of the proof of Proposition 3 is improved. Statement of Lemma 5 is rephrased. Version 3: Acknowledgement of financial support is added. Accepted for publication in "Stochastic Partial Differential Equations: Analysis and Computations

Multi-valued, singular stochastic evolution inclusions

We provide an abstract variational existence and uniqueness result for multi-valued, monotone, non-coercive stochastic evolution inclusions in Hilbert spaces with general additive and Wiener multiplicative noise. As examples we discuss certain singular diffusion equations such as the stochastic 1-Laplacian evolution (total variation flow) in all space dimensions and the stochastic singular fast diffusion equation. In case of additive Wiener noise we prove the existence of a unique weak-* mean ergodic invariant measure.Comment: 39 pages, in press: J. Math. Pures Appl. (2013

Improved regularity for the stochastic fast diffusion equation

We prove that the solution to the singular-degenerate stochastic fast-diffusion equation with parameter $m\in (0,1)$, with zero Dirichlet boundary conditions on a bounded domain in any spatial dimension, and driven by linear multiplicative Wiener noise, exhibits improved regularity in the Sobolev space $W^{1,m+1}_0$ for initial data in $L^{2}$.Comment: 7 pages, 29 reference

Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise

We aim at studying a novel mathematical model associated to a physical phenomenon of infiltration in an homogeneous porous medium. The particularities of our system are connected to the presence of a gravitational acceleration term proportional to the level of saturation, and of a Brownian multiplicative perturbation. Furthermore, the boundary conditions intervene in a Robin manner with the distinction of the behavior along the inflow and outflow respectively. We provide qualitative results of well-posedness, the investigation being conducted through a functional approach

Berries as a case study for crop wild relative conservation, use, and public engagement in Canada

Conservation of plant biodiversity, in particular crop wild relatives including those tended and cultivated by Indigenous Peoples, is critical to food security and agricul ture. Building on the 2019 road map for crop wild relatives, we examine berries as a case study for crop wild relative conservation, use, and public engagement. We focus on berries due not only to their economic, cultural, and nutritional importance but also because they are consumed fresh, providing a unique opportunity for individuals and communities to connect with plants. We outline health benefits, geographic dis tribution, and species at risk for Canadian berries. We describe practices, strategies, and approaches used by Indigenous Peoples to steward berries and emphasize the importance of traditional knowledge. We highlight opportunities for in situ and ex situ berry conservation and use of berries in plant breeding and Indigenous foodways. Our aim is to lay the groundwork for future collaborative efforts in these areas and to showcase berries as a useful case study for conservation of food plant biodiversity and public engagement

Existence and uniqueness of the solution for stochastic super-fast diffusion equations with multiplicative noise

International audienceIn this paper we prove an existence and uniqueness result for the stochastic porous media equation with very singular diffusion and multiplicative noise, by using monotonicity techniques. The multiplicative Gaussian noise is essential in the proof of existence