NON - LINEAR STOCHASTIC PDEs

Stochastic Non Linear Poisson Equation

Application - Statistics of potential fields for protein in solvents (Protein Interactions)
The nonlinear Poisson-Boltzmann equation (nPBE) is an elliptic partial differential equation used in applications such as protein interactions and biophysical chemistry (among many others). It describes the nonlinear electro- static potential of charged bodies submerged in an ionic solution. The kinetic presence of the solvent molecules introduces randomness to the shape of a protein, and thus a more accurate model that incorporates these random perturbations of the domain is analyzed to compute the statistics of quantities of interest of the solution.