Formulas in the inverse problem for the kinetic equation (Q1363948)

The author considers the multidimensional nonlinear inverse problem for the kinetic equation, which consists of the determination of two functions, \(w(\overline x,\overline p,t)\) and \(\lambda (x,t)\) \((\partial\lambda/ \partial p_j=0\), \(j=1,2, \dots, n)\), \((\overline x, \overline p,t) \in D\subset \mathbb{R}^{2n+1}\), \(\overline x\in\mathbb{R}^n\), \(\overline p\in\mathbb{R}^n\), \(t\in \mathbb{R}\), where \(D\) is a region in the Euclidean space \(\mathbb{R}^{2n+1}\), \(n\geq 1\), containing the point \(\overline x= \overline 0\), subject to the conditions \[ {\partial w\over \partial t}+ \sum^n_{j=1} {\partial w\over \partial x_j} p_j= \lambda (\overline x,t) f(\overline p,w), \quad w|_{\overline x=\overline 0} =Q(\overline p,t),\;(\overline p,t)\in D^0=D \cap \{\overline x= \overline 0\}, \] where the continuous functions \(f(\overline p,y)\), \(y\in \mathbb{R}\), \(Q(\overline p,t)\) are specified.