Unique continuation and an inverse problem for hyperbolic equations across a general hypersurface

Unique Continuation and an Inverse Problem for Hyperbolic Equations across a General Hypersurface

For a hyperbolic equation p(x, t)∂ t u(x, t) = ∆u(x, t)+ ∑n j=1 qj(x, t)∂ju+ qn+1(x, t)∂tu+r(x, t)u in R n×R with p ∈ C and q1, ...., qn+1, r ∈ L∞, we consider the unique continuation and an inverse problem across a non-convex hypersurface Γ. Let Γ be a part of the boundary of a domain and let ν(x) be the inward unit normal vector to Γ at x. Then we prove the unique continuation near a point x0...

A timelike Cauchy problem and an inverse problem for general hyperbolic equations

Analytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

analytic solutions for the stephen's inverse problem with local boundary conditions including elliptic and hyperbolic equations

in this paper, two inverse problems of stephen kind with local (dirichlet) boundary conditions are investigated. in the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. for the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

On an Inverse Hyperbolic Problem

We consider the inverse problem of recovery of an initial condition of a hyperbolic PDE. This problem is also called sometimes “thermoacoustic tomography”. In the past publications both stability estimates and convergent numerical methods for this problem were obtained only under some restrictive conditions imposed on the principal part of the elliptic operator. In this paper logarithmic stabil...