Logarithmic Convexity and impulse Approximate Controllability for Degenerate Parabolic Equations with Robin Boundary Conditions

2025/05/06 by Baggari, Hind El, Ouelddris, Ilham
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2505.03663

Abstract

In this work, we investigate the approximate controllability of a class of one-dimensional degenerate parabolic equations with Robin boundary conditions. The degeneracy occurs at one endpoint of the spatial domain, and we apply an impulsive control in a small region at a fixed moment. Our main result establishes an observability inequality for the adjoint system, from which we deduce approximate controllability at final time . The proof relies on a logarithmic convexity argument, developed through a Carleman commutator approach.

Citations

• On the existence and uniqueness of solutions for non-autonomous semi-linear systems with non-instantaneous impulses, delay, and non-local conditions
• Qualitative properties for the 1-D Impulsive Wave Equation: Controllability and Observability
• Observation estimate for the heat equations with Neumann boundary condition via logarithmic convexity
• Carleman commutator approach in logarithmic convexity for parabolic equations
• Controllability of impulse controlled systems of heat equations coupled by constant matrices

Related

• Boundary controllability for a 1D degenerate parabolic equation with a Robin boundary condition
• Numerical impulse controllability for parabolic equations by a penalized HUM approach
• Controllability of a system of non-autonomous degenerate coupled parabolic equations
• Boundary controllability for a coupled system of degenerate/singular parabolic equations
• Null controllability of n-dimensional parabolic equations degenerated on partial boundary