• Corpus ID: 229332255

The stochastic $p$-Laplace equation on $\mathbb{R}^d$

  title={The stochastic \$p\$-Laplace equation on \$\mathbb\{R\}^d\$},
  author={Kerstin Schmitz and Aleksandra Zimmermann},
We show well-posedness of the p -Laplace evolution equation on R d with square integrable random initial data for arbitrary 1 < p < ∞ and arbitrary space dimension d ∈ N . The noise term on the right-hand side of the equation may be additive or multiplicative. Due to a lack of coercivity of the p -Laplace operator in the whole space, the possibility to apply well-known existence and uniqueness theorems in the classical functional setting is limited to certain values of 1 < p < ∞ and also… 


Quasilinear SPDEs via Rough Paths
  • F. Otto, H. Weber
  • Mathematics
    Archive for Rational Mechanics and Analysis
  • 2018
AbstractWe are interested in (uniformly) parabolic PDEs with a nonlinear dependence of the leading-order coefficients, driven by a rough right hand side. For simplicity, we consider a space-time
Multiplicative stochastic heat equations on the whole space
We carry out the construction of some ill-posed multiplicative stochastic heat equations on unbounded domains. The two main equations our result covers are, on the one hand the parabolic Anderson
Non-linear rough heat equations
This article is devoted to define and solve an evolution equation of the form dyt = Δytdt + dXt (yt), where Δ stands for the Laplace operator on a space of the form $${L^p(\mathbb R^n)}$$, and X is a
On a nonlinear parabolic problem arising in some models related to turbulent flows
This paper studies the Cauchy–Dirichlet problem associated with the equation \[ b(u)_t - {\operatorname{div}}\left( {| {\nabla u - K(b(u)){\bf e}} |^{p - 2} (\nabla u - K(b(u)){\bf e})} \right) +
We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough
Homogeneous diffusion in ℝ with power-like nonlinear diffusivity
AbstractWe study the nonnegative solutions of the initial-value problem ut=(ur|ux|p-1ux)x,u(x, 0)∈L1(ℝ), where p>0, r+p>0. The local velocity of propagation of the solutions is identified as V = -vx|
Exponential time integrators for stochastic partial differential equations in 3D reservoir simulation
This work investigates exponential time integrators, in conjunction with an upwind weighted finite volume discretisation in space, for the efficient and accurate simulation of advection–dispersion processes including non-linear chemical reactions in highly heterogeneous 3D oil reservoirs.
An infinite dimensional stochastic differential equation with state spaceC(ℝ)
SummaryWe consider a time evolution of unbounded continuous spins on the real line. The evolution is described by an infinite dimensional stochastic differential equation with local interaction.
Stochastic langevin model for flow and transport in porous media.
A new model is presented, which employs smoothed particle hydrodynamics to solve a Langevin equation for flow and dispersion in porous media, which allows for effective separation of the advective and diffusive mixing mechanisms, which is absent in the classical dispersion theory.
One dimensional stochastic partial differential equations and the branching measure diffusion
SummaryAn existence theorem in the spirit of Keisler [Ke], is proved for the simple one-dimensional diffusion equation driven by white noise modulated by a non-linear function of the solution. This