A boundary value problem in the hyperbolic space

A Boundary Value Problem in the Hyperbolic Space

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...

A Well-Posed Free Boundary Value Problem for a Hyperbolic Equation with Dirichlet Boundary Conditions

We construct solutions of a free boundary value problem for a hyperbolic equation with Dirichlet boundary data. This problem arises from a model of deformation of granular media.

On the Boundary Value Problem in a Dihedral Angle for Normally Hyperbolic Systems of First Order

Some structural properties as well as a general threedimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of function...

Riemann Boundary Value Problem for Triharmonic Equation in Higher Space

We mainly deal with the boundary value problem for triharmonic function with value in a universal Clifford algebra: Δ(3)[u](x) = 0, x ∈ R (n)\∂Ω, u (+)(x) = u (-)(x)G(x) + g(x), x ∈ ∂Ω, (D (j) u)(+)(x) = (D (j) u)(-)(x)A j + f j (x), x ∈ ∂Ω, u(∞) = 0, where (j = 1,…, 5)  ∂Ω is a Lyapunov surface in R (n) , D = ∑ k=1 (n) e k (∂/∂x k) is the Dirac operator, and u(x) = ∑ A e A u A (x) are unknown ...