Well posedness of a nonlinear mixed problem for a parabolic equation with integral condition

Abstract

Abstract The aim of this work is to prove the well posedness of some posed linear and nonlinear mixed problems with integral conditions. First, an a priori estimate is established for the associated linear problem and the density of the operator range generated by the considered problem is proved by using the functional analysis method. Subsequently, by applying an iterative process based on the obtained results for the linear problem, the existence, uniqueness of the weak solution of the nonlinear problems is established.

Keywords

• Energy inequality
• Integral boundary conditions
• Strong solution
• Weak solution
• Second order parabolic equation