In [FoT], Foias and Temam introduced a method for estimating the space-analyticity radius of solutions of the Navier Stokes equation with periodic boundary conditions. For the numerous applications, see e.g. [CEES, CRT, DTH, FT, Gr, K, LO]. In our previous paper [GK], we did not use the Fourier series and were thus able to treat the Navier Stokes and other semilinear parabolic equations with si...

The Solow model is an economic model to describe economic growth. In this thesis we will provide an extension to this model by introducing a space dimension into the model and a production function that is non-concave. Furthermore, we will consider different kinds of technological progress. The resulting model is governed by a semilinear parabolic partial differential equation which describes t...

The main goal of the present paper is to define the solution operator (ξ, g) 7→ u associated to the evolution equation du = (Au)dt + dg, u(0) = ξ, where A generates a C0-semigroup in a Banach space X, ξ ∈ X, g ∈ BV ([ a, b ];X), and to study its main properties, such as regularity, compactness, and continuity. Some necessary and/or sufficient conditions for the compactness of the solution opera...

We investigate the positive solutions of the semilinear parabolic system with coupled nonlinear nonlocal sources subject to weighted nonlocal Dirichlet boundary conditions. The blow-up and global existence criteria are obtained.

This paper studies the rst order necessary conditions for the optimal controls of semilinear and quasilinear parabolic partial di erential equations with pointwise state constraints. Pontryagin type maximum principle is obtained.

We discuss an optimal control problem of laser surface hardening of steel which is governed by a dynamical system consisting of a semilinear parabolic equation and an ordinary differential equation with a non differentiable right hand side function f+. To avoid the numerical and analytic difficulties posed by f+, it is regularized using a monotone Heaviside function and the regularized problem ...