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In this paper, we discuss the solvability of the nonlinear parabolic systems associated to the nonlinear parabolic equation: \(\frac{\partial b_{i}(x,u_{i})}{\partial t} -div(a(x,t,u_{i},\nabla u_{i}))- \phi_{i}(x,t,u_{i})) +f_{i}(x,u_{1},u_{2})=0\) where the function  \(b_{i}(x,u_{i})\) verifies some regularity conditions, the term \(\Big(a(x,t,u_{i},\nabla u_{i})\Big)\) is a generalized Leray-Lions operator and \(\phi_{i}\) is a Caratheodory function assumed to be  Continuous on \(u_i\) and satisfy only a…

The aim of this paper is to study the boundary enlarged gradient controllability problem governed by parabolic evolution equations. The purpose is to find and compute the control \(u\) which steers the gradient state from an initial gradient one \(\nabla y_{_{0}}\) to a gradient vector supposed to be unknown between two defined bounds \(b_1\) and…