eISSN:

2163-2480

## Evolution Equations & Control Theory

December 2017 , Volume 6 , Issue 4

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**Abstract:**

We deal with the simultaneous controllability properties of two one dimensional (strongly) coupled wave equations when the control acts on the boundary. Necessary and sufficient conditions for approximate and exact controllability are proved.

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**Abstract:**

The controllability of non-autonomous evolution systems is an important and difficult topic in control theory. In this paper, we study the approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay. The theory of linear evolution operators is used instead of

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**Abstract:**

We investigate the effectiveness of a simple finite-dimensional feedback control scheme for globally stabilizing solutions of infinite-dimensional dissipative evolution equations introduced by Azouani and Titi in [

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**Abstract:**

A game control problems of the Schlögl and FitzHugh-Nagumo equations are considered. The problems are investigated both from the viewpoint of the first player (the partner) and of the second player (the opponent). For both players, their own procedures for forming feedback controls are specified.

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**Abstract:**

We consider the large time behavior of a solution to a drift-diffusion equation for degenerate and non-degenerate type. We show an instability and uniform unbounded estimate for the semi-linear case and uniform bound and convergence to the stationary solution for the case of mass critical degenerate case for higher space of dimension bigger than two.

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**Abstract:**

This paper deals with exact controllability of a class of abstract nonlocal Cauchy problem with impulsive conditions in Banach spaces. By using Sadovskii fixed point theorem and Mönch fixed point theorem, exact controllability results are obtained without assuming the compactness and Lipschitz conditions for nonlocal functions. An example is given to illustrate the main results.

*+*[Abstract](1048)

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**Abstract:**

We consider the large time behavior of solutions to the following nonlinear wave equation:

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**Abstract:**

In this paper, we investigate the initial boundary value problem for the linearized double dispersion equation on the half space

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