Tatsien Li

SEMI-GLOBAL C1 SOLUTION TO THE MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

By means of an equivalent invariant form of boundary conditions, the author get the existence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with general nonlinear boundary conditions.

LOCAL EXACT BOUNDARY CONTROLLABILITY FOR A CLASS OF QUASILINEAR HYPERBOLIC SYSTEMS

For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems, this paper establishes the local exact boundary controllability with boundary controls only acting on one end. As an application, the authors show the local exact boundary controllability for a kind of nonlinear vibrating string problem.

Life–span of classocal solutions to fully nonlinear wave equations

In an unified and simple way we get lower bounds of the life-span of classical solutions to the Cauchy problems for fully nonlinear wave equaitons of the form kappav;u=F(u,Du,DxDu) for the space dimension n 3

Exact Synchronization for a Coupled System of Wave Equations with Dirichlet Boundary Controls

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.

The mixed initial-boundary value problem for reducible quasilinear hyperbolic systems with linearly degenerate characteristics

In this paper, we prove that the C0 boundedness of solution implies the global existence and uniqueness of C1 solution to the mixed initial-boundary value problem for linearly degenerate, reducible quasilinear hyperbolic systems with nonlinear boundary conditions and we show by an example that the C0 norm of solution may blow up in a finite time. This gives the mechanism of the formation of singularities caused by the interaction of boundary conditions with nonlinear hyperbolic waves. The same result is still valid for the quasilinear hyperbolic system of rich type.

Exact Controllability for First Order Quasilinear Hyperbolic Systems with Zero Eigenvalues

For a class of mixed initial-boundary value problem for general quasilinear hyperbolic systems with zero eigenvalues, the authors establish the local exact controllability with boundary controls acting on one end or on two ends and internal controls acting on a part of equations in the system.

Global propagation of regular nonlinear hyperbolic waves

In this work we shall consider the nonlinear hyperbolic waves described by the following Cauchy problem for first order quasilinear hyperbolic systems

Global exact boundary controllability for first order quasilinear hyperbolic systems of diagonal form

\left\{ \matrix{ {{\partial u} \over {\partial t}} + {\rm A}\left( u \right){{\partial u} \over {\partial x}} = 0, \hfill \cr t = 0:u = \varphi \left( x \right), \hfill \cr} \right.