On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity

Yuliya Mishura; Kostiantyn Ralchenko; Mounir Zili

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arXiv · 2009.11915

On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity

Yuliya Mishura·Kostiantyn Ralchenko·Mounir Zili

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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.

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Yuliya Mishura, Kostiantyn Ralchenko, Mounir Zili. 2020-09-24. On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity. https://arxiv.org/abs/2009.11915

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