Uniqueness of determination of coefficients of quasilinear parabolic equation (Q797065)

The author's aim is to find functions (u(x,t), a(x,t,u)), satisfying the conditions: \[ u_ t-(a(x,t,u)u_ x)_ x+f(x,t,u)=0,\quad 0<t<T,\quad 0<x<1, \] \[ a(x,t,u)u_ x+h_ j(t,u)u=q_ j(t),\quad 0<t<T,\quad x=j,\quad j=0,1, \] u(0,x)\(=0\), \(0<x<1\), and the additional condition \(u(t,\ell)=g(t)\), \(0<t<T\), where \(\ell\) is a number from [0,1]. The author proves the uniqueness of (u,a) and of solutions of some similar problems. Remark: Clearly it is impossible to find a function of three variables a(t,x,u) from given data so the author's proof fails, because the equation (17) of this paper is unsolvable, and its coefficient equals to \(a_ 1(t,x) (u_ 2-u_ 1)^{-1}\), where \(u_ 2\), \(u_ 1\) are possible solutions of the mentioned problem.