Mixed boundary value problems for nonstrict hyperbolic equations

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,...

Mixed Two-point Boundary-value Problems for Impulsive Differential Equations

In this article, we prove the existence of solutions to mixed twopoint boundary-value problem for impulsive differential equations by variational methods, in both resonant and the non resonant cases.

Boundary value problems for mixed type equations and applications

Initial-Boundary Value Problem for Hyperbolic Equations

where Ji = 0 for x0 < 0. The problem is to find necessary and sufficient conditions on B(x, B) such that the initial-boundary value problem (1), (2), (3) is well-posed. Note that all theorems that a;re formulated below will also apply to the case when (1) is a general hyperbolic equation or a hyperbolic system of equations of arbitrary order provided that all components of the characteristic co...

The hyperbolic region for hyperbolic boundary value problems

The well-posedness of hyperbolic initial boundary value problems is linked to the occurrence of zeros of the so-called Lopatinskii determinant. For an important class of problems, the Lopatinskii determinant vanishes in the hyperbolic region of the frequency domain and nowhere else. In this paper, we give a criterion that ensures that the hyperbolic region coincides with the projection of the f...