In this talk we consider a free boundary problem describing a change of the length of a one-dimensional elastic material. By elementary calculation the free boundary problem is given as the initial boundary value problem for the hyperbolic equation with dynamic boundary condition. Moreover, as the practical example for the elastic material we deal with a new mathematical model for a valve made ...

Symmetric hyperbolic systems with nonhomogeneous conservative boundary conditions are considered. Existence, uniqueness, and regularity are established for the boundary value problem and the initial-boundary value problem. This boundary problem is not strongly well-posed in L2, a loss of derivatives is observed. Minimal regularity assumptions on the coefficients of the operator are made.

1. Solution of a two-point boundary value problem. We consider a linear dynamical system ˙ x = Ax, with x(t) ∈ R n. There is an n-dimensional subspace of solutions of this equation, so to single out one of the trajectories we can impose, roughly speaking, n equations. In the most common situation, we specify x(0) = x 0 , in which case the unique solution is x(t) = e tA x 0. This is called an in...

We consider the initial-boundary value problem of two-dimensional inviscid heat conductive Boussinesq equations with nonlinear heat diffusion over a bounded domain with smooth boundary. Under slip boundary condition of velocity and the homogeneous Dirichlet boundary condition for temperature, we show that there exists a unique global smooth solution to the initial-boundary value problem for H i...