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Article
A Note on the Indirect Controls for a Coupled System of Wave Equations
By a procedure of successive projections, the authors decompose a coupled system of wave equations into a sequence of sub-systems. Then, they can clarify the indirect controls and the total number of controls....
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Article
On the Synchronizable System
In this paper, the synchronizable system is defined and studied for a coupled system of wave equations with the same wave speed or with different wave speeds.
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Article
On the sensitivity of the transmission of boundary dissipation for strongly coupled and indirectly damped systems of wave equations
We consider the stability of a system of two strongly coupled wave equations by means of only one boundary feedback. We show that the stability of the system depends in a very complex way on all of the involve...
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Chapter
Exact Boundary Controllability and Non-exact Boundary Controllability
Since the exact synchronization on a finite time interval is closely linked with the exact boundary null controllability, we first consider the exact boundary controllability and the non-exact boundary nul...
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Chapter
Necessity of the Conditions of \(C_p\)-Compatibility
In this chapter, we will discuss the necessity of the conditions of \(C_p\)-compatibility for system (III) with coupled Robin boundary controls. This problem is closely related to the number of applied boundary c...
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Chapter
Exactly Synchronizable States
When system (I) possesses the exact boundary synchronization, the corresponding exactly synchronizable states will be studied in this chapter.
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Chapter
Some Algebraic Lemmas
In order to study the approximate boundary synchronization for system (III) with coupled Robin boundary controls, some algebraic lemmas are given in this chapter.
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Chapter
Approximate Boundary Synchronization by p-Groups
The boundary by p-groups is introduced and studied in this chapter for system (III) with coupled Robin controls.
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Chapter
Exactly Synchronizable States by p-Groups
When system (I) possesses the exact synchronization by p-groups, the corresponding exactly synchronizable states by p-groups will be studied in this chapter.
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Chapter
Unique Continuation for Robin Problems
We consider the unique for Robin problems in this chapter.
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Chapter
Closing Remarks
Some closing remarks including related literatures and prospects are given in this chapter.
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Chapter
Approximate Boundary Synchronization
The approximate boundary synchronization is defined and studied in this chapter for system (I) with Dirichlet boundary controls.
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Chapter
Exact Boundary Synchronization and Non-exact Boundary Synchronization
In the case of partial lack of boundary , we consider the exact boundary synchronization and the non-exact boundary in this chapter for system (II) with Neumann boundary controls.
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Chapter
Determination of Exactly Synchronizable States by p-Groups
When system (II) possesses the exact boundary synchronization by p-groups, the corresponding exactly synchronizable states by p-groups will be studied in this chapter.
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Chapter
Approximate Boundary Synchronization
The approximate boundary synchronization is defined and studied in this chapter for system (II) with Neumann boundary controls.
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Chapter
Exact Boundary Synchronization
Based on the results of the exact boundary controllability and the non-exact boundary controllability, we study the exact boundary synchronization for system (III) with coupled Robin boundary controls.
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Chapter
Algebraic Preliminaries
This chapter contains some algebraic preliminaries, which are useful in the whole book. In this chapter, we denote by A a matrix of order N, by D a full column-rank matrix of order \(N\times M\) with $$M\leqslant...
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Chapter
Preliminaries on Problem (III) and (III0)
In order to consider the exact boundary and the exact boundary synchronization of system (III), we first give some necessary results on problem (III) and (III0) in this chapter.
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Chapter
Exact Boundary Synchronization by p-Groups
The exact boundary synchronization by groups will be considered in this chapter for system (III) with further lack of coupled Robin boundary controls.
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Chapter
Exact Boundary Synchronization and Non-exact Boundary Synchronization
In the case of partial lack of boundary controls, we consider the exact boundary synchronization and the non-exact boundary synchronization in this chapter for system (I) with Dirichlet boundary controls.
