Well-posedness of hyperbolic initial boundary value problems

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 ...

Well-posedness for Hyperbolic Problems

Tariel Kiguradze ON SOLVABILITY AND WELL-POSEDNESS OF INITIAL–BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER NONLINEAR HYPERBOLIC EQUATIONS

The sufficient conditions for unique local solvability, global solvability and of well-posedness of initial-boundary value problems for higher order nonlinear hyperbolic equations are studied.

L-WELL-POSEDNESS OF 3D div-curl BOUNDARY VALUE PROBLEMS

Criteria for the existence and uniqueness of weak solutions of div-curl boundary-value problems on bounded regions in space with C-boundaries are developed. The boundary conditions are either given normal component of the field or else given tangential components of the field. Under natural integrability assumptions on the data, finite-energy (L) solutions exist if and only if certain compatibi...

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,...