Sur une classe de problèmes aux limites pour équations aux dérivées partielles avec conditions aux bords non standards

Abstract

In this work, we study a mixed problem with an integral space variable condition for a parabolic equation of mixed type. The existence and uniqueness of the solution in functional weighed Sobolev space are proved. The proof is based on two sided a priori estimates and the density of the range of the operator generated by the considered problem.