On the solvability of a class of singular parabolic equations with nonlocal boundary conditions in nonclassical function spaces - Abdelfatah Bouziani (International Journal of Mathematics and Mathematical Sciences)
The aim of this paper is to prove the existence, uniqueness, and continuous dependence upon the data of a generalized solution for certain singular parabolic equations with initial and nonlocal boundary conditions. The proof is based on an a priori estimate established in nonclassical function spaces, and on the density of the range of the operator corresponding to the abstract formulation of the considered problem.