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

Author

Listed:
  • Mishura, Yuliya
  • Ralchenko, Kostiantyn
  • Zili, Mounir

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.

Suggested Citation

  • Mishura, Yuliya & Ralchenko, Kostiantyn & Zili, Mounir, 2020. "On mild and weak solutions for stochastic heat equations with piecewise-constant conductivity," Statistics & Probability Letters, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:stapro:v:159:y:2020:i:c:s0167715219303281
    DOI: 10.1016/j.spl.2019.108682
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