Nonlinear partial differential equations provide the continuum language for systems whose response depends on their current state.
Published · Transactions of the American Mathematical Society, 379 (2026) 4, pp. 2343-2383. The stochastic thin-film equation with mobility exponent $n\in [\frac{8}{3},3)$ on the one-dimensional torus with multiplicative Stratonovich noise is considered. We show that martingale solutions exist for non-negative initial values. This advances on…
Published · Communications on pure and applied mathematics, 78 (2025) 9, pp. 1609-1655. The problem of deriving a gradient flow structure for the porous medium equation which is {\em thermodynamic}, in that it arises from the large deviations of some microscopic particle system, is studied…
Published · Journal of functional analysis, 286 (2024) 4, p. 110269. The long-time behavior of stochastic Hamilton-Jacobi equations is analyzed, including the stochastic mean curvature flow as a special case. In a variety of settings, new and sharpened results are obtained. Among them…
Published · The annals of probability, 52 (2024) 5, pp. 1903-1953. Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-diffusion equations are proven. The treatment includes reaction potentials with degenerate minima. The proof relies on an asymptotic expansion of the…
