Existence, Uniqueness and Homogenization of Nonlinear Parabolic Problems with Dynamical Boundary Conditions in Perforated Media


We consider a nonlinear parabolic problem with nonlinear dynamical boundary conditions of pure-reactive type in a media perforated by periodically distributed holes of size \(\varepsilon \). The novelty of our work is to consider a nonlinear model where the nonlinearity also appears in the boundary. The existence and uniqueness of solution is analyzed. Moreover, passing to the limit when \(\varepsilon \) goes to zero, a new nonlinear parabolic problem defined on a unified domain without holes with zero Dirichlet boundary condition and with extra terms coming from the influence of the nonlinear dynamical boundary conditions is rigorously derived.

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Correspondence to María Anguiano.

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This work was completed with the support of Junta de Andalucía (Spain), Proyecto de Excelencia P12-FQM-2466.

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Anguiano, M. Existence, Uniqueness and Homogenization of Nonlinear Parabolic Problems with Dynamical Boundary Conditions in Perforated Media. Mediterr. J. Math. 17, 18 (2020). https://doi.org/10.1007/s00009-019-1459-y

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  • Homogenization
  • perforated media
  • dynamical boundary conditions

Mathematics Subject Classification

  • Primary 35B27
  • Secondary 35K57