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On The Construction Of A Potential From Cauchy Data, Lester Caudill, Bruce D. Lowe
On The Construction Of A Potential From Cauchy Data, Lester Caudill, Bruce D. Lowe
Department of Math & Statistics Faculty Publications
We investigate the problem of recovering a potential q(y)in the differential equation:
-∆u+q(y)u = 0, (x, y) ∈ (0, 1) x (0, 1),
u(0, y) = u(1, y) = u(x, 0) = 0,
u(x, 1) = f(x), uy(x, 1) = g(x).
The method of separation of variables reduces the recovery of q(y) to a nonstandard inverse Sturm-Liouville problem. An asymptotic formula is developed that suggests that under appropriate conditions on the Cauchy pair (f, g), q(y) is uniquely determined up to the mean. Moreover, the recovery of …