Abdelwahab Zarour, Chahla Latrous, Ameur Memour

On the Solvability of a Non-Local Problem with Integral Boundary Condition for a Second Order Parabolic Equation

abstract:
In this paper, the existence and uniqueness of a strong solution of a second order parabolic equation with integral boundary condition is proved. First, we establish a priori estimate and prove that the range of the operator generated by the considered problem is dense. The technique of deriving the a priori estimate is based on the construction of a suitable multiplicator. From the resulted energy estimate, it is possible to establish the solvability of the linear problem.

Mathematics Subject Classification: 35B45, 35G10

Key words and phrases: Energy inequality, integral boundary conditions, strong solution, second order parabolic equation