We consider the controllability of a chemotaxis system of parabolic–elliptic type. By linearizing the nonlinear system into two separate linear equations, we can bypass the obstacle caused by the nonlinear drift term and establish local null controllability of the original nonlinear system. This approach is different from the usual method for dealing with coupled parabolic systems. © 2013 Elsev...

We present a noncausal framework for model-based feedback stabilization of a large class of spatially developing boundary-layer 'ow systems. The systems considered are (approximately) parabolic in the spatial coordinate x. This facilitates the application of a range of established feedback control theories which are based on the solution of di6erential Riccati equations which march over a 8nite...

We present an abstract framework for semilinear parabolic problems based on analytic semigroup theory. The same framework is used for numerical discretization based on the finite element method. We prove local existence of solutions and local error estimates. These are applied in the context of dynamical systems. The framework is also used to analyze the finite element method for a stochastic p...

A system modeling the thermoelastic bards contacts is studied. The problem is first transformed into an equivalent nonlocal parabolic systems using a transformation, and then the existence and uniqueness of the solutions are demonstrated via the theoretical potential representation theory of the parabolic equations. Finally some realistic situations in the applications are discussed using the r...

The properties of ω-limit set and global asymptotic behavior are first obtained for asymptotically autonomous discrete dynamical processes on metric spaces.Then certain equivalence of the asymptotic behavior between an asymptotically periodic semiflows and its associated asymptotically autonomous discrete dynamical process is proved. As some applications, the global behavior of asymptotically p...

Various optimization problems associated with the optimal control of distributed parabolic systems with time delays appearing in boundary conditions were studied recently by Wang (1975), Knowles (1978), Kowalewski (1988; 1990a;1990b; 1998; 1999; 2001), Kowalewski and Duda (1992) and Kowalewski and Krakowiak (2000). In (Wang, 1975), optimal control problems for parabolic systems with Neumann bou...

This paper is devoted to establishing local and global existence theorems for autonomous semilinear parabolic initial value problems. The local existence theorems do not require Lipchitz condition on nonlinear term. The global existence theorem is an extension of the well-known result of Fujita-Weissler for semilinear heat equations to general autonomous semilinear parabolic equations and systems.

We study the existence of optimal controls for problems governed by semilinear parabolic equations. The nonlinearities in the state equation need not be monotone and the data need not be regular. In particular, the control may be any bounded Radon measure. Our examples include problems with nonlinear boundary conditions and parabolic systems.

DESCRIPTION Concentrating Solar Power (CSP), also referred to as solar thermal power, uses mirrors to concentrate the sun's rays to heat a fluid that is then used to generate electricity, often using conventional steam turbines. There are three primary CSP technologies: parabolic trough, solar tower, and dish engine. The most common CSP system is the parabolic trough, which uses curved mirrors ...

In this paper, we derive W 1,∞ and piecewise C1,α estimates for solutions, and their t-derivatives, of divergence form parabolic systems with coefficients piecewise Hölder continuous in space variables x and smooth in t. This is an extension to parabolic systems of results of Li and Nirenberg [Comm Pure Appl Math, 2003, 56: 892–925] on elliptic systems. These estimates depend on the shape and t...