Finite-time transition to intermittency for a stochastic heat equation driven by the square of a Gaussian field
Abstract
Abstract In this paper, we study the spatial behavior of the solution ψ ( x , t ) to the stochastic heat equation ∂ t ψ ( x , t ) − 1 2 ∂ x 2 2 ψ ( x , t ) = g S ( x , t ) 2 ψ ( x , t ) , with 0 ⩽ t ⩽ T , x ∈ R , and ψ ( x , 0 ) = 1 . Here, g > 0 is a coupling constant and S ( x , t ) is a stationary, homogeneous, and ergodic Gaussian field. Focusing on E ( x , g ) ≡ ψ ( x , T ) at a finite time T > 0 , we identify the critical coupling g c ( T )
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Theoretical and Computational Physics
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Journal of Physics A Mathematical and Theoretical
- Volume
- 59
- Issue
- 37
- Pages
- 375204–375204
- Publication date
- 8 September 2026
- Language
- EN