Stability for an inverse problem for a two-speed hyperbolic PDE in one space dimension

作者：Rakesh^*; Sacks Paul

来源：Inverse Problems, 2010, 26(2): 025005.

DOI：10.1088/0266-5611/26/2/025005

Suppose A(x), B(x) are 2 x 2 matrices on an interval [0,infinity) and C is a constant diagonal matrix with distinct positive entries. Let U(x, t) be the matrix solution of the system of hyperbolic PDEs CU(tt)-U(xx)-AU(x)-BU = 0 on [0,infinity) x R with the initial condition U(., t) = 0 for t < 0 and the boundary condition U(0, t) = delta(t)I(2). We prove a stability result for the inverse problem of recovering A, B from U(x)(0,.). The solutions of the forward problem propagate with two different speeds so techniques for inverse problems for a single hyperbolic PDE are not applicable in any obvious way.

• 出版日期2010-2