  The well-posedness of the growth-coagulation equation is established for
coagulation kernels having singularity near the origin and growing atmost
linearly at infinity. The existence of weak solutions is shown by means of the
method of the characteristics and a weak $L_1$-compactness argument. For the
existence result, we also show our gratitude to Banach fixed point theorem and
a refined version of the Arzel\'{a}-Ascoli theorem. In addition, the continuous
dependence of solutions upon the initial data is shown with the help of the
DiPerna-Lions theory, Gronwall's inequality and moment estimates. Moreover, the
uniqueness of solution follows from the continuous dependence. The results
presented in this article extend the contributions made in earlier literature.
