An inverse problem for the heat equation

[摘要] Let u(t) = u(xx) - q(x)u, 0 less than or equal to x less than or equal to 1, t > 0, u(0, t) = 0, u(1, t) = a(t), u(x, 0) = 0, where a(t) is a given function vanishing for t > T, a(t) not equal 0, integral(0)(T) a(t) dt < infinity, Suppose one measures the flux u(x)(0, t) := b(0)(t) for all t > 0. Does this information determine q(x) uniquely? Do the measurements of the flux u(x)(1, t) := b(t) give more information about q(x) than b(0)(t) does? These questions are answered in this note. (C) 2001 Elsevier Science.

[发布日期] 2001-12-15