Local null controllability for a parabolic equation with local and nonlocal nonlinearities in moving domains

André da Rocha Lopes; Juan Límaco

doi:10.3934/eect.2021024

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2022, Volume 11, Issue 3: 749-779. Doi: 10.3934/eect.2021024

This issue Previous Article Exponential stability for a multi-particle system with piecewise interaction function and stochastic disturbance Next Article The lifespan of solutions for a viscoelastic wave equation with a strong damping and logarithmic nonlinearity

Local null controllability for a parabolic equation with local and nonlocal nonlinearities in moving domains

André da Rocha Lopes^1, , and
Juan Límaco^2,

1.
Departamento de Análise Matemática, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ, 20550-900, Brazil
2.
Departamento de Matemática Aplicada, Universidade Federal Fluminense, Niterói, RJ, 24020-140, Brazil

^* Corresponding author: andre.lopes@ime.uerj.br
^* Corresponding author: andre.lopes@ime.uerj.br

Received: June 30, 2020

Revised: January 31, 2021

Published: June 2022

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Abstract

In this paper, we establish a local null controllability result for a nonlinear parabolic PDE with local and nonlocal nonlinearities in a domain whose boundary moves in time by a control force with a multiplicative part acting on a prescribed subdomain. We prove that, if the initial data is sufficiently small and the linearized system at zero satisfies an appropriate condition, the equation can be driven to zero.

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Mathematics Subject Classification: Primary: 35K65, 93B05; Secondary: 35K55, 93C20.

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