Local null controllability for degenerate parabolic equations with nonlocal term. (October 2018)

• Record Type: Journal Article
• Authors: Demarque, R.; Límaco, J.; Viana, L.
• Is Part Of: Nonlinear analysis. Volume 43(2018)
• Page Start: 523
• Page End: 547
• Publication Date: 2018-10
• Subjects: Degenerate parabolic equations -- Controllability -- Nonlinear parabolic equations -- Nonlocal term; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.04.001
• Languages: English
• ISSNs: 1468-1218

Abstract

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.