Local null controllability for degenerate parabolic equations with nonlocal term. (October 2018) - Demarque, R.; Límaco, J.; Viana, L.
Abstract: We establish a local null controllability result for following nonlinear parabolic equation: u t − b x, ∫ 0 1 u u x x + f ( t, x, u ) = h χ ω, ( t, x ) ∈ ( 0, T ) × ( 0, 1 ) where b ( x, r ) = ℓ ( r ) a ( x ) is a function with separated variables that defines an operator which degenerates at x = 0 and has a nonlocal term. Our approach relies on an application of Liusternik's inverse mapping theorem that demands the proof of a suitable Carleman estimate.