On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity
Probability
2020-09-28 v1
Abstract
We investigate a stochastic partial differential equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by a space-time white noise. We introduce a notion of weak solution of this equation and prove its equivalence to the already known notion of mild solution.
Keywords
Cite
@article{arxiv.2009.11915,
title = {On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity},
author = {Yuliya Mishura and Kostiantyn Ralchenko and Mounir Zili},
journal= {arXiv preprint arXiv:2009.11915},
year = {2020}
}
Comments
13 pages