Removability of isolated singularities of solutions of quasilinear parabolic equations with absorption

This paper is devoted to the investigation of solutions with point singularities for a general quasilinear parabolic equation with absorption. A method for the derivation of new pointwise estimates of a solution and integral estimates of its gradient is developed. Precise conditions on the behaviour of the term characterizing the absorption in the equation that ensure the non-existence of solutions with point singularities are established. The cases of solutions with singularities in the initial plane and in the interior of the domain are considered.