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1.
In this paper, the authors consider the inverse piston problem for the system of one-dimensional isentropic flow and obtain that, under suitable conditions, the piston velocity can be uniquely determined by the initial state of the gas on the right side of the piston and the position of the forward shock.  相似文献
2.
This paper deals with the blow-up phenomenon, particularly, the geometric blow-up mechanism, of classical solutions to the Cauchy problem for quasilinear hyperbolic systems in the critical case. We prove that it is still the envelope of the same family of characteristics which yields the blowup of classical solutions to the Cauchy problem in the critical case.  相似文献
3.
In this paper, the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced. By means of the exact null controllability of a reduced coupled system, under certain conditions of compatibility, the exact synchronization, the exact synchronization by groups, and the exact null controllability and synchronization by groups are all realized by suitable boundary controls.  相似文献
4.
In this paper,the authors define the strong (weak) exact boundary controllability and the strong (weak) exact boundary observability for first order quasilinear hyperbolic systems,and study their properties and the relationship between them.  相似文献
5.
Preface     
Jacques-Louis Lions (1928-2001) was an exceptional mathematician, whose lasting influence is still deeply felt all over the world.He was a universally recognized and admired expert in partial differential equations, to the study of which he has made outstanding contributio  相似文献
6.
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Tatsien LI Fanghua LIN Guiqiang CHEN Xiaoming WANG Professor Andrew Majda is one of the most prominent applied mathematicians in the world. He is well-known for both his seminal theoretical contributions to partial differential equations and his diverse and fundamental contributions to many applied areas such as scattering theory, shock waves, combustion, incompressible flow, vortex motion, turbulent diffusion and atmosphere ocean science.  相似文献
7.
This paper concerns a system of equations describing the vibrations of a planar network of nonlinear Timoshenko beams.The authors derive the equations and appropriate nodal conditions,determine equilibrium solutions and,using the methods of quasilinear hyperbolic systems,prove that for tree-like networks the natural initial-boundary value problem admits semi-global classical solutions in the sense of Li [Li,T.T.,Controllability and Observability for Quasilinear Hyperbolic Systems,AIMS Ser.Appl.Math.,vol 3,American Institute of Mathematical Sciences and Higher Education Press,2010] existing in a neighborhood of the equilibrium solution.The authors then prove the local exact controllability of such networks near such equilibrium configurations in a certain specified time interval depending on the speed of propagation in the individual beams.  相似文献
8.
This paper first shows the exact boundary controllability for a coupled system of wave equations with Neumann boundary controls.In order to establish the corresponding observability inequality,the authors introduce a compact perturbation method which does not depend on the Riesz basis property,but depends only on the continuity of projection with respect to a weaker norm,which is obviously true in many cases of application.Next,in the case of fewer Neumann boundary controls,the non-exact boundary controllability for the initial data with the same level of energy is shown.  相似文献
9.
In this Note, we consider a system of wave equations coupled by a nilpotent matrix with homogeneous Dirichlet boundary condition. We establish the uniqueness of the solution when partial Neumann observation satisfies Kalman's rank condition.  相似文献
10.
By equivalently replacing the dynamical boundary condition by a kind of nonlocal boundary conditions, and noting a hidden regularity of solution on the boundary with a dynamical boundary condition, a constructive method with modular structure is used to get the local exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献
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