THE DETERMINATION OF MULTIPLE COEFFICIENTS IN A 2ND-ORDER DIFFERENTIAL-EQUATION FROM INPUT SOURCES
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abstract
The authors consider the question of recovering the coefficients a and q from the equation -(a(x)u'j(x))'+q(x)uj(x)=f j(x) with boundary conditions uj(0)=uj(1)=0, and where the non-homogeneous source terms (fj(x))j=1infinity form a basis for L2(0,1). They prove that a unique determination is possible from data measurements (a(0)u'j(0), a(1)u'j(1))j=1infinity. An algorithm that allows efficient numerical reconstruction of a(x) and q(x) from finite data is given.
