  We study the inverse problem of recovering a semilinear diffusion term
$a(t,\lambda)$ as well as a quasilinear convection term $\mathcal
B(t,x,\lambda,\xi)$ in a nonlinear parabolic equation
$$\partial_tu-\textrm{div}(a(t,u) \nabla u)+\mathcal B(t,x,u,\nabla
u)\cdot\nabla u=0, \quad \mbox{in}\ (0,T)\times\Omega,$$ given the knowledge of
the flux of the moving quantity associated with different sources applied at
the boundary of the domain. This inverse problem that is modeled by the
solution dependent parameters $a$ and $\mathcal B$ has many physical
applications related to various classes of cooperative interactions or complex
mixing in diffusion processes. Our main result states that, under suitable
assumptions, it is possible to fully recover the nonlinear diffusion term $a$
as well as the nonlinear convection term $\mathcal B$. The recovery of the
diffusion term is based on the idea of solutions to the linearized equation
with singularities near the boundary $\partial \Omega$. Our proof of the
recovery of the convection term is based on the idea of higher order
linearization to reduce the inverse problem to a density property for certain
anisotropic products of solutions to the linearized equation. We show this
density property by constructing sufficiently smooth geometric optic solutions
concentrating on rays in $\Omega$.
