Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 15, pp. 1-22.

Title: Null-controllability for 1-D degenerate quasilinear parabolic equations

Authors: Pitagoras P. de Carvalho (Univ. Estadual do Piaui, Teresina, PI, Brazil)
         Reginaldo Demarque (Univ. Federal Fluminense, Rio das Ostras, RJ, Brazil)
         Juan Limaco (Univ. Federal Fluminense,  Niteroi, RJ, Brazil)
         Luiz Viana  (Univ. Federal Fluminense,  Niteroi, RJ, Brazil)
  
Abstract:
In this article, we prove local null-controllability for 
one-dimensional degenerate quasilinear parabolic equations. We apply 
a well-known local inversion argument used by Fursikov and Imanuvilov. 
The strategy is to use Carleman estimates, previously 
obtained for weak and strong degenerate parabolic problems.   

Submitted June 2, 2024. Published February 19, 2025.
Math Subject Classifications: 35K65, 35K59, 93B05, 35K55.
Key Words: Degenerate parabolic equations; quasilinear parabolic equations; controllability; nonlinear parabolic equations.