Resumen de Stochastic heat equation with rough dependence in space

Yaozhong Hu, Jingyu Huang, Khoa Lê, David Nualart Rodón, Samy Tindel

• This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H∈(14,12)H∈(14,12) in the space variable. The existence and uniqueness of the solution uu are proved assuming the nonlinear coefficient σ(u)σ(u) is differentiable with a Lipschitz derivative and σ(0)=0σ(0)=0.