Multilevel Picard iterations for solving smooth semilinear parabolic heat equations

Determining nodes for semilinear parabolic equations

We discuss the uniqueness of the equilibria of time-global solutions of general semilinear parabolic equations by a finite set of values of these solutions. More precisely, if the asymptotic behaviour of a time-global solution is known on an appropriate finite set, then the asymptotic behaviour of a time-global solution itself is entirely determined in a domain.

Matematica – Existence for semilinear parabolic stochastic equations

Abstract The boundary value problem for semilinear parabolic stochastic equations of the form dX − ∆X dt + β(X)dt 3 QdWt, where Wt is a Wiener process and β is a maximal monotone graph everywhere defined, is well posed.

Analysis of preconditioned Picard iterations for the Navier-Stokes equations

Multilevel Adaptive Methods for Semilinear Equations

Optimal Control of Nonsmooth, Semilinear Parabolic Equations

This paper is concerned with an optimal control problem governed by a semilinear, nonsmooth operator differential equation. The nonlinearity is locally Lipschitz-continuous and directionally differentiable, but not Gâteaux-differentiable. Two types of necessary optimality conditions are derived, the first one by means of regularization, the second one by using the directional differentiability ...