By means of the existence and uniqueness of semi-global C1 solution to the mixed initial boundary value problem with general nonlinear boundary conditions for first order quasi linear hyperbolic systems with zero eigenvalues, we establish the local exact boundary controllability for second order quasilinear hyperbolic systems with general nonlinear boundary conditions.
In this paper, sufficient conditions are obtained for the oscillation of all solutions of the homogeneous Neumann, Dirichlet and Robin's boundary value problems associated with the hyperbolic system
The mixed initial-boundary value problem for a kind of the first order quasilinear hyperbolic system with nonlinear boundary conditions in a half-unbounded domain {(t,x)|t≥0,x≥0} is considerded.
The global existence theorem of C~∞ solution for the initial-boundary problem for quasilinear symmetric hyperbolic system has been proved by the method of the convergence of infinity and the structure of dissipation.
Taking the problem of smoothing the discontinuous selfsimilar solutions of the system of hyperbolic equations as a research background, in the paper we have discussed the asymptotic expansion of the solution of the equation of second order with a small parameter ε>0 εu″= F (ξ, u)u′ which satisfies the boundary value conditions u(±∞)=u~±(ε), where u~±(0)
In this paper, the mixed initial-boundary value problem for general first order quasilinear hyperbolic systems with nonlinear boundary conditions in the domain D = {(t, x) | t ≥ 0, x ≥ 0} is considered.
If the system is a symmetric hyperbolic system [2, 3], then the extrema of the entropy production at the discontinuity correspond to extrema of the velocity.
An explicit finite-difference scheme of second order of accuracy [1] was used for the numerical integration of the hyperbolic system of equations, which was written in divergence form.
In this paper we study the Goursat problem for semilinear hyperbolic equations with zero boundary condition where the boundary is the characteristic cone for hyperbolic operator.
In this paper we review our some results about the strongly singular (discontinuous, measure, or delta function) problems for nonlinear hyperbolic equations.