Hyperbolic initial-boundary value problems in two unknowns

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

Initial Boundary Value Problems for Hyperbolic Partial Differential Equations

1, Differential equations in one space dimension. The simplest hyperbolic differential equation is given by (1.1) du/dt = cdu/dx, where c is a constant, Its general solution is u(x, t) — F(x + ci), i.e., it is constant along the "characteristic lines" x + ct = const (see Figure 1). Therefore, if we u(l,t) = g(t) u(0,t)*g(t want to determine the solution of (1.1) in the region 0 ^ x ^ 1, t ja 0,...

Well-posedness of hyperbolic Initial Boundary Value Problems

Assuming that a hyperbolic initial boundary value problem satsifies an a priori energy estimate with a loss of one tangential derivative, we show a well-posedness result in the sense of Hadamard. The coefficients are assumed to have only finite smoothness in view of applications to nonlinear problems. This shows that the weak Lopatinskii condition is roughly sufficient to ensure well-posedness ...

Hermite methods for hyperbolic initial-boundary value problems

We study arbitrary-order Hermite difference methods for the numerical solution of initial-boundary value problems for symmetric hyperbolic systems. These differ from standard difference methods in that derivative data (or equivalently local polynomial expansions) are carried at each grid point. Time-stepping is achieved using staggered grids and Taylor series. We prove that methods using deriva...

approximating initial-value problems with two-point boundary-value problems: bbm-equation