Perturbation methods for inverse problems related to degenerate differential equations. (English) Zbl 1343.34049

From the introduction: Consider the simplest case of evolution problem described by \[ {dy\over dt}= Ay+ f(t)z,\quad 9\leq t\leq\tau,\tag{1} \]
\[ y(0)= y_0\in D(A).\tag{2} \] Our goal is to identify the solution-pair \((y,f)\), where \(y\) is the solution to (1), (2) and \(f\in C([0, \tau], \mathbb{C})\), under the additional information \[ \Phi[y(t)]= g(t),\;0\leq t\leq\tau, \] where \(\Phi\in X^*\), the dual space of \(X\), and \(g\in C([0,\tau],\mathbb{C})\).


34A55 Inverse problems involving ordinary differential equations
34G10 Linear differential equations in abstract spaces