On the solvability of a class of nonlinear singular parabolic equation with integral boundary condition

In this paper, the existence and uniqueness of a weak solution for nonlinear singular parabolic equation with integral boundary conditions is proved. First, the associated linear problem is solved. After writing the linear problem on its operatorial form, we establish an a priori bound from which we deduce the uniqueness of the strong solution. For the solvability of the associated linear problem, we prove that the range of the operator generated by the considered problem is dense. On the basis of the obtained results of the linear problem, we apply an iterative process to establish the existence and uniqueness of the weak solution of the nonlinear problem.