Further study of spatial decay estimates for semilinear parabolic equations

Blow-up Estimates for Higher-order Semilinear Parabolic 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.

Error Estimates for Spatially Discrete Approximations of Semilinear Parabolic Equations with Initial Data of Low Regularity

Semidiscrete finite element methods for a semilinear parabolic equation in Rd, d < 3, were considered by Johnson, Larsson, Thomée, and Wahlbin. With h the discretization parameter, it was proved that, for compatible and bounded initial data in Ha, the convergence rate is essentially 0(h2+a) for t positive, and for a = 0 this was seen to be best possible. Here we shall show that for 0 < a < 2 th...

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 ...